Elimination of the linearization error and improved basis-set convergence within the FLAPW method

We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies $E_l$ and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters $E_l$ and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions $u_l(r,E)$ to the scalar-relativistic approximation of the radial Dirac equation with $E>E_l$ and (ii) constructed from second energy derivatives $\partial^2 u_l(r,E) / \partial E^2$ at $E=E_l$. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW+lo approach, which requires an extra set of LOs to reach the same total energy, though.Comment: 12 pages, 15 figure

Comparison between exact and semilocal exchange potentials: An all-electron study for solids

The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and NiO). This is done in the framework of the linearized augmented plane-wave method, which allows for a very accurate all-electron solution of electronic structure problems in solids. In order to assess the ability of the semilocal potentials to approximate the EXX-OEP, we considered the EXX total energy, electronic structure, electric-field gradient, and magnetic moment. An attempt to parameterize a semilocal exchange potential is also reported

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

The optimized-effective-potential (OEP) method is a special technique to construct local Kohn-Sham potentials from general orbital-dependent energy functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Bl\"ugel, A. G\"orling, Phys. Rev. B 83, 045105 (2011)] we showed that uneconomically large basis sets were required to obtain a smooth local potential without spurious oscillations within the full-potential linearized augmented-plane-wave method (FLAPW). This could be attributed to the slow convergence behavior of the density response function. In this paper, we derive an incomplete-basis-set correction for the response, which consists of two terms: (1) a correction that is formally similar to the Pulay correction in atomic-force calculations and (2) a numerically more important basis response term originating from the potential dependence of the basis functions. The basis response term is constructed from the solutions of radial Sternheimer equations in the muffin-tin spheres. With these corrections the local potential converges at much smaller basis sets, at much fewer states, and its construction becomes numerically very stable. We analyze the improvements for rock-salt ScN and report results for BN, AlN, and GaN, as well as the perovskites CaTiO3, SrTiO3, and BaTiO3. The incomplete-basis-set correction can be applied to other electronic-structure methods with potential-dependent basis sets and opens the perspective to investigate a broad spectrum of problems in theoretical solid-state physics that involve response functions.Comment: 17 pages, 7 figures, 3 table

Local exact exchange potentials within the all-electron FLAPW method and a comparison with pseudopotential results

We present a general numerical approach to construct local Kohn-Sham potentials from orbital-dependent functionals within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method, in which core and valence electrons are treated on an equal footing. As a practical example, we present a treatment of the orbital-dependent exact-exchange (EXX) energy and potential. A formulation in terms of a mixed product basis, which is constructed from products of LAPW basis functions, enables a solution of the optimized-effective-potential (OEP) equation with standard numerical algebraic tools and without shape approximations for the resulting potential. We find that the mixed product and LAPW basis sets must be properly balanced to obtain smooth and converged EXX potentials without spurious oscillations. The construction and convergence of the exchange potential is analyzed in detail for diamond. Our all-electron results for C, Si, SiC, Ge, GaAs semiconductors as well as Ne and Ar noble-gas solids are in very favorable agreement with plane-wave pseudopotential calculations. This confirms the adequacy of the pseudopotential approximation in the context of the EXX-OEP formalism and clarifies a previous contradiction between FLAPW and pseudopotential results.Comment: 12 pages, 7 figures, 5 table

Les conseils du département du Bas-Rhin pendant la Révolution

L’article établit une liste précise des membres des assemblées et exécutifs départementaux du département pendant la Révolution (soit 17 institutions). Une étude prosopographique tente d’en faire une typologie. Les « hommes de lois » d’Ancien régime y furent majoritaires, ce qui assure aussi la prépondérance des catholiques. Puis à partir de la Terreur, on voit apparaître des professions nouvelles, où le nombre de luthériens est plus important. Les biographies de quelques « conseillers » considérés comme représentatifs sont présentés.First of all, this article produces a precise and exhaustive list of the members of the departement assemblies and executives. A prosopographical study establishes that Ancien Régime administrators and lawyers – mostly catholics – made up the majority of the first assemblies, logicaly because the administrative functions were reserved to catholics. But in 1793, the professions seem to be more mixed, and we see more protestants in the assemblies. A few biographies considered to be « representative » conclude the article.Der Artikel stellt eine genaue Liste der Mitglieder der Versammlungen und Exekutiven des Departement während der Revolution (insgesamt 17 Institutionen) auf. Eine prosographische Studie schließt darauf, dass die Juristen des alten Regimes mehrheitlich waren, so dass die Katholiken überwiegend waren. Mit der Schreckenherrschaft (Terreur) erscheinen neue Berufe, wo die Anzahl der Lutheraner größer ist. Einige repräsentativen Biographien werden dargestellt

Muller (Claude), « La liberté ou la mort ». L’Alsace et la Révolution

Voilà un ouvrage qui aborde la Révolution en Alsace d’une façon peu commune. Plutôt que de se noyer dans un fatras documentaire pléthorique, Claude Muller a choisi une voie moins aride, plus difficile aussi, celle de la relation de l’Alsace à la Révolution, ou, plus précisément, celle de la recherche de réponses à la question : comment les Alsaciens de l’époque ont-ils ressenti cet épisode ? Pour animer ce vaste débat, il a fait appel à des témoins contemporains pris parmi ceux ayant laissé m..

Hybrid functionals within the all-electron FLAPW method: implementation and applications of PBE0

We present an efficient implementation of the PBE0 hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schroedinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone (BZ) sum over vector-matrix-vector products. We show that the Coulomb matrix can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including oxide materials, where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.Comment: 15 pages, 6 figures, 2 table

Renormalization of effective interactions in a negative charge-transfer insulator

We compute from first principles the effective interaction parameters appropriate for a low-energy description of the rare-earth nickelate LuNiO$_{3}$ involving the partially occupied $e_g$ states only. The calculation uses the constrained random-phase approximation and reveals that the effective on-site Coulomb repulsion is strongly reduced by screening effects involving the oxygen-$p$ and nickel-$t_{2g}$ states. The long-range component of the effective low-energy interaction is also found to be sizeable. As a result, the effective on-site interaction between parallel-spin electrons is reduced down to a small negative value. This validates effective low-energy theories of these materials proposed earlier. Electronic structure methods combined with dynamical mean-field theory are used to construct and solve an appropriate low-energy model and explore its phase diagram as a function of the on-site repulsion and Hund's coupling. For the calculated values of these effective interactions we find, in agreement with experiments, that LuNiO$_{3}$ is a metal without disproportionation of the $e_g$ occupancy when considered in its orthorhombic structure, while the monoclinic phase is a disproportionated insulator.Comment: 10 pages, 4 figure

Housing market stability, mortgage market structure, and monetary policy: Evidence from the euro area

This paper investigates how monetary policy stance and mortgage market structure affect non-fundamental house price movements in eleven Euro area countries. Based on a three-stage approach, our empirical evidence suggests that a one-time monetary-easing shock can significantly trigger house price booms in Euro area countries with liberal mortgage markets. Such shocks can explain over 20% of the forecasting error variance of non-fundamental house price runups in Ireland and Spain. We find that, in countries with more regulated mortgage markets, monetary policy stance does not significantly affect non-fundamental house prices. Policymakers may wish to focus on limiting mortgage equity withdrawals and on monitoring loan-to-value ratios and tax policies in order to minimize the side effects of accommodative monetary policies on housing market stability for Euro area countries. We posit that this is especially true for peripheral countries, which are more likely to be subjected to overly loose monetary policy stances

Phonons from Density-Functional Perturbation Theory using the All-Electron Full-Potential Linearized Augmented Plane-Wave Method FLEUR

Phonons are quantized vibrations of a crystal lattice that play a crucial role in understanding many properties of solids. Density functional theory (DFT) provides a state-of-the-art computational approach to lattice vibrations from first-principles. We present a successful software implementation for calculating phonons in the harmonic approximation, employing density-functional perturbation theory (DFPT) within the framework of the full-potential linearized augmented plane-wave (FLAPW) method as implemented in the electronic structure package FLEUR. The implementation, which involves the Sternheimer equation for the linear response of the wave function, charge density, and potential with respect to infinitesimal atomic displacements, as well as the setup of the dynamical matrix, is presented and the specifics due to the muffin-tin sphere centered LAPW basis-set and the all-electron nature are discussed. As a test, we calculate the phonon dispersion of several solids including an insulator, a semiconductor as well as several metals. The latter are comprised of magnetic, simple, and transition metals. The results are validated on the basis of phonon dispersions calculated using the finite displacement approach in conjunction with the FLEUR code and the phonopy package, as well as by some experimental results. An excellent agreement is obtained.Comment: 44 pages, 6 figure