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

Koopmans-compliant functionals and their performance against reference molecular data

Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional functionals can then be constructed that modify the potential energy surface, including e.g. Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G$_0$W$_0$ and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations (Note: Supplemental Material is included in the source)

Variational Minimization of Orbital-dependent Density Functionals

Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density dependent, and provide a very promising avenue to go beyond density-functional theory, especially when studying electronic, optical and dielectric properties, charge-transfer excitations, and molecular dissociations. Unlike conventional density functionals, these functionals are not invariant under unitary transformations of occupied electronic states, which leave the total charge density intact, and this added complexity has greatly inhibited both their development and their practical applicability. Here, we first recast the minimization problem for non-unitary invariant energy functionals into the language of ensemble density-functional theory, decoupling the variational search into an inner loop of unitary transformations that minimize the energy at fixed orbital subspace, and an outer-loop evolution of the orbitals in the space orthogonal to the occupied manifold. Then, we show that the potential energy surface in the inner loop is far from convex parabolic in the early stages of the minimization and hence minimization schemes based on these assumptions are unstable, and present an approach to overcome such difficulty. The overall formulation allows for a stable, robust, and efficient variational minimization of non-unitary-invariant functionals, essential to study complex materials and molecules, and to investigate the bulk thermodynamic limit, where orbitals converge typically to localized Wannier functions. In particular, using maximally localized Wannier functions as an initial guess can greatly reduce the computational costs needed to reach the energy minimum while not affecting or improving the convergence efficiency.Comment: 10 pages, 6 figure

On Green's function embedding using sum-over-pole representations

In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. This latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form $\text{Tr}_\omega \text{Ln}\left\{G_0^{-1}G\right\}$, where $\text{Tr}_\omega$ is the frequency integration of the trace operator. Here, we show that using a sum-over-pole representation for the Green's functions and the algorithmic-inversion method one can obtain in full generality an explicit analytical expression for $\text{Tr}_\omega \text{Ln}\left\{G_0^{-1}G\right\}$. This allows one, e.g., to derive a variational expression for the Klein functional in the presence of an embedding bath, or to provide an explicit expression of the RPA correlation energy in the framework of the optimized effective potential.Comment: 11 pages, 3 figure

\u201cPlay the City. Geografi a della \u201ccitt\ue0 amatoriale\u201d: teorie, applicazioni, prospettive\u201d

Our article is divided into three connected sections. The first one discusses the image of the city in amateur movies, taking into account the cinematic urban archeology of home movies and operational practices of databases, Geographical Information Systems, maps, installations. We propose the notion of \u201camateur city\u201d as the synthesis of multiple, located views collected in a long period of time projected onto a map. The second section describes the Play the City app, a digital tool to map and navigate the urban space, between the past and the present, through 120 clips of amateur filmmakers. The third part deals with the idea of mapping the \u201cstoryworld\u201d of a city through the app and opens up some theoretical perspectives on film images and geo-located systems

Same same but different: Code-Switching in Schweizer SMS – ein Vergleich zwischen vier Sprachen

This study examines the formal and functional aspects of code-switching (CS) in a Swiss corpus of 26'000 text messages (SMS). Four corpora (Swiss-German, French, Italian and Romansh) are compared with regard to the absolute number of CS, the languages used for CS, the grammatical properties of the CS elements and their potential functions. The aim is to find out: a) which patterns are representative of one or more individual lan-guages and b) which patterns are characteristic for SMS-communication in general and/or are valid for Switzerland as a whole. With regard to the differences in the number of CS and the languages used, the respective patterns seem to mirror the different lan-guage contact situations in Switzerland. As for the described CS-types, the corpora under scrutiny seem to share the extensive use of one-token alternations (isolated items) that carry out framing functions and may point out a shared type of minimal multilingual practice

Donor and acceptor levels of organic photovoltaic compounds from first principles

Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductors has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans' condition [Phys. Rev. B 82, 115121 (2010)] is apt at describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost.Comment: 13 pages, 11 figure

Neurophysiological Findings in Neuronal Ceroid Lipofuscinoses

Neuronal ceroid lipofuscinoses (NCLs) are a heterogeneous group of neurodegenerative diseases, characterized by progressive cerebral atrophy due to lysosomal storage disorder. Common clinical features include epileptic seizures, progressive cognitive and motor decline, and visual failure, which occur over different time courses according to subtypes. During the latest years, many advances have been done in the field of targeted treatments, and in the next future, gene therapies and enzyme replacement treatments may be available for several NCL variants. Considering that there is rapid disease progression in NCLs, an early diagnosis is crucial, and neurophysiological features might have a key role for this purpose. Across the different subtypes of NCLs, electroencephalogram (EEG) is characterized by a progressive deterioration of cerebral activity with slowing of background activity and disappearance of spindles during sleep. Some types of heterogeneous abnormalities, diffuse or focal, prevalent over temporal and occipital regions, are described in many NCL variants. Photoparoxysmal response to low-frequency intermittent photic stimulation (IPS) is a typical EEG finding, mostly described in CLN2, CLN5, and CLN6 diseases. Visual evoked potentials (VEPs) allow to monitor the visual functions, and the lack of response at electroretinogram (ERG) reflects retinal neurodegeneration. Taken together, EEG, VEPs, and ERG may represent essential tools toward an early diagnosis of NCLs