Koopmans-compliant spectral functionals for extended systems

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation - i.e. on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans' orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state-of-the-art in diagrammatic techniques (self-consistent many-body perturbation theory with vertex corrections), notably using just a functional formulation for spectral properties and the physics of the generalized-gradient approximation; when ionization potentials are compared, the results are roughly twice as accurate.Comment: 9 pages, 3 figures, 1 supporting informatio

Screening in orbital-density-dependent functionals

Electronic-structure functionals that include screening effects, such as Hubbard or Koopmans' functionals, require to describe the response of a system to the fractional addition or removal of an electron from an orbital or a manifold. Here, we present a general method to incorporate screening based on linear-response theory, and we apply it to the case of the orbital-by-orbital screening of Koopmans' functionals. We illustrate the importance of such generalization when dealing with challenging systems containing orbitals with very different chemical character, also highlighting the simple dependence of the screening on the localization of the orbitals. We choose a set of 46 transition-metal complexes for which experimental data and accurate many-body perturbation theory calculations are available. When compared to experiment, results for ionization potentials show a very good performance with a mean absolute error of $~0.2$ eV, comparable to the most accurate many-body perturbation theory approaches. These results reiterate the role of Koopmans' compliant functionals as simple and accurate quasiparticle approximations to the exact spectral functional, bypassing diagrammatic expansions and relying only on the physics of the local density or generalized-gradient approximation

Exchange and correlation energy in the adiabatic connection fluctuation-dissipation theory beyond RPA

Density functional theory (DFT) within standard local density/generalized gradient approximations (LDA/GGAs) have been proved to succesfully predict the properties of a wide class of electronic systems at a reasonable computational time. However there exist a number of situations in wich DFT within LDA/GGAs qualitatively fails. One of such problems is their inability, due their intrinsic local nature, to describe long-range interaction between non overlapping molecular fragments, or weakly bound systems such as molecules about to break during a chemical reaction. The Adiabatic Connection Fluctuation Dissipation (ACFD) formalism tackle this kind of problems at a very foundamental level providing a perfect starting point for the development of truly non-local functionals. We have indeed developed and implemented an efficient scheme for the calculation of the correlation energy via the ACFD theorem going beyond the random phase approximation (RPA) by including the exact-exchange contribution to the kernel. We found that this contribution plays a crucial role for a correct and accurate description of the total energy of an electronic system without compromising the achivements of the original RPA functional

High-accuracy determination of the neutron flux in the new experimental area n_TOF-EAR2 at CERN

A new high flux experimental area has recently become operational at the n_TOF facility at CERN. This new measuring station, n_TOF-EAR2, is placed at the end of a vertical beam line at a distance of approximately 20m from the spallation target. The characterization of the neutron beam, in terms of flux, spatial profile and resolution function, is of crucial importance for the feasibility study and data analysis of all measurements to be performed in the new area. In this paper, the measurement of the neutron flux, performed with different solid-state and gaseous detection systems, and using three neutron-converting reactions considered standard in different energy regions is reported. The results of the various measurements have been combined, yielding an evaluated neutron energy distribution in a wide energy range, from 2meV to 100MeV, with an accuracy ranging from 2%, at low energy, to 6% in the high-energy region. In addition, an absolute normalization of the n_TOF-EAR2 neutron flux has been obtained by means of an activation measurement performed with 197Au foils in the beam.Comisión Europea FP7/2007-2011 No.605203Centro Nacional de Ciencias de Polonia UMO- 2012/04/M/ST2/00700Centro Nacional de Ciencias de Polonia UMO-2016/22/M/ST2/00183Fundación de Ciencia Croata No. 168

Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of any orbital. In crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy to a ground state provides a set of minimizing variational orbitals that are localized and thus break the periodicity of the underlying lattice. Despite this, we show that Bloch symmetry can be preserved and it is possible to describe the electronic states with a band-structure picture, thanks to the Wannier-like character of the variational orbitals. We also present a method to unfold and interpolate the electronic bands from supercell ($\Gamma$-point) calculations, which enables us to calculate full band structures with Koopmans-compliant functionals. The results obtained for a set of benchmark semiconductors and insulators show very good agreement with state-of-the-art many-body perturbation theory and experiments, underscoring the reliability of these spectral functionals in predicting band structures.Comment: 34 pages, 4 figure

The deviation angle for one-lane roundabouts: A general mathematical formulation and application

Abstract Properly designed roundabouts may lead to safety improvements based on both reducing approaching speeds and controlling traffic. Measurements of deflection of vehicle trajectories are commonly used to estimate roundabout speed control. One of these measurements is the deviation angle, which is mentioned in both the Italian and Swiss road standards and, in specific conditions, can be more effective than other methods. This article presents a general mathematical formulation for linking several geometric parameters with the deviation angle in different rural and urban one-lane roundabout configurations, which is currently missing in the literature. For urban roundabouts, refuge islands for pedestrians and cyclists were considered. Based on the proposed formulation, a sensitivity analysis of the influential geometric parameters was conducted. Results suggest that an insufficient deflection of trajectories (deviation angle less than 45°) is always present for roundabouts with inscribed circle diameter less than 25 m; for urban roundabouts with refuge islands for pedestrians and cyclists having inscribed circle diameter less than 34 m and orthogonal legs; and for roundabouts with angles between opposite legs smaller than 140°. The main parameters which are responsible for a decrease in the deviation angle are: a decrease in the inscribed circle diameter; a decrease in the angle between opposite legs; and an increase in the width of the circulatory lane. Some optimized procedures for roundabout design, the generalized application of the deviation angle method and alternative speed control measures in cases of small deviation angles are discussed

Beyond the random phase approximation with a local exchange vertex

With the aim of constructing an electronic structure approach that systematically goes beyond the GW and random phase approximation (RPA) we introduce a vertex correction based on the exact-exchange (EXX) potential of time-dependent density functional theory. The EXX vertex function is constrained to be local but is expected to capture similar physics as the Hartree-Fock vertex. With the EXX vertex, we then unify different beyond-RPA approaches such as the various resummations of RPA with exchange and the second-order screened exchange approximation. The theoretical analysis is supported by numerical studies on the hydrogen dimer and the electron gas, and we discuss the role of including the vertex correction in both the screened interaction and the self-energy. Finally, we give details on our implementation within the plane-wave pseudo potential framework and demonstrate the excellent performance of the different RPA with exchange methods in describing the energetics of hydrogen and van der Waals bonds

Investigating the Deviation Angle Method for Ensuring Deflection at One-Lane Rural Roundabouts

Roundabouts developed as a road intersection design option has resulted in a series of nonuniform design guidance criteria in Europe, as well as in the United States and other Countries. In addition to different design specifications about the geometry of the elements constituting a roundabout (width and lanes of the circulatory roadway, entry and exit legs, splitter island), the methods for guaranteeing that vehicle paths deflect through the roundabout are also different. These methods ensure proper travel speeds between conflicting traffic flows. Currently, the main parameters used by standards to control the deflection are the deflection radius, the entry path radius, and the deviation angle. After a comparison between International deflection methods for roundabouts, this study checks the geometric requirements of the deviation angle for more than 7.000 hypothetical one-lane rural roundabouts. The Computer-Aided Design (CAD) drawing of the roundabouts takes into account the range of variability of their main geometric parameters, according to the Italian Standard. Subsequently, a number of the considered roundabouts checked with both the entry path radius and the German methods. Some results showing the greater effectiveness of the less popular deviation angle method are discussed. The main aims of this paper are:1) to promote the deviation angle method, which is only used in Switzerland and Italy;2) to improve standards, as regards the applicability and validity of the deflection angle method;3) to help practitioners to know in advance the outcome of the deflection checks at the beginning of the iterative design process, once the boundary conditions are known

Geometric Design Issues and Safety Analysis of Two-way Rural Road Tunnels

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