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Über dieses Buch

The series Topics in Current Chemistry presents critical reviews of the present and future trends in modern chemical research. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field. Review articles for the individual volumes are invited by the volume editors. Readership: research chemists at universities or in industry, graduate students.

Inhaltsverzeichnis

Frontmatter

Electronic and Optical Properties of Dye-Sensitized TiO2 Interfaces

Abstract
Dye-sensitized solar cells (DSCs) represent a promising approach to the direct conversion of sunlight to electrical energy at low cost and high efficiency. DSCs are based on a film of anatase TiO2 nanoparticles covered by adsorbed molecular dyes and immersed in a liquid redox electrolyte. Upon photoexcitation of the chemisorbed dye, electrons are injected into the TiO2 conduction band and can travel across the nanostructured film to reach the counter-electrode, while the oxidized dye is regenerated by the redox electrolyte. In this review we present a summary of recent computational studies of the electronic and optical properties of dye-sensitized TiO2 interfaces, with the aim of providing the basic understanding of the operation principles of DSCs and establishing the conceptual basis for their design and optimization.
We start with a discussion of isolated dyes in solution, focusing on the dye’s atomic structure, ground and excited state oxidation potentials, and optical absorption spectra. We examine both Ru(II)-polypyridyl complexes and organic “push-pull” dyes with a D-π-A structure, where the donor group (D) is an electron-rich unit, linked through a conjugated linker (π) to the electron-acceptor group (A). We show that a properly calibrated computational approach based on Density Functional Theory (DFT) combined with Time Dependent DFT (TD-DFT) can provide a good description of both the absorption spectra and ground and excited state oxidation potential values of the Ru(II) complexes. On the other hand, organic push-pull dyes are not well described by the standard DFT/TD-DFT approach. For these dyes, an excellent description of the electronic structure in gas phase can be obtained by the many body perturbation theory GW method, which has, however, a much higher computational cost.
We next consider interacting dye/semiconductor systems. Key properties are the dye adsorption structure onto the semiconductor, the nature and localization of the dye@semiconductor excited states, and the alignment of ground and excited state energy levels at the dye/semiconductor heterointerface. These properties, along with an estimate of the electronic coupling, constitute the fundamental parameters that determine the electron injection and dye regeneration processes. For metallorganic dyes, standard DFT/TDDFT methods are again found to reproduce accurately most of the relevant electronic and optical properties. For highly conjugated organic dyes, characterized by a high degree of charge transfer excited states, instead, the problems associated to the charge-transfer nature of their excited states extend to their interaction with TiO2 and translate into an erroneous description of the relative energetics of dye/semiconductor excited states. A full description of push-pull organic dyes/semiconductor excited states, which is essential for modeling the key process of electron injection in DSCs, still represents a challenge which should be addressed by next generation DFT or post-DFT methods.
Mariachiara Pastore, Annabella Selloni, Simona Fantacci, Filippo De Angelis

Status in Calculating Electronic Excited States in Transition Metal Oxides from First Principles

Abstract
Characterization of excitations in transition metal oxides is a crucial step in the development of these materials for photonic and optoelectronic applications. However, many transition metal oxides are considered to be strongly correlated materials, and their complex electronic structure is challenging to model with many established quantum mechanical techniques. We review state-of-the-art first-principles methods to calculate charged and neutral excited states in extended materials, and discuss their application to transition metal oxides. We briefly discuss developments in density functional theory (DFT) to calculate fundamental band gaps, and introduce time-dependent DFT, which can model neutral excitations. Charged excitations can be described within the framework of many-body perturbation theory based on Green’s functions techniques, which predominantly employs the GW approximation to the self-energy to facilitate a feasible solution to the quasiparticle equations. We review the various implementations of the GW approximation and evaluate each approach in its calculation of fundamental band gaps of many transition metal oxides. We also briefly review the related Bethe–Salpeter equation (BSE), which introduces an electron–hole interaction between GW-derived quasiparticles to describe accurately neutral excitations. Embedded correlated wavefunction theory is another framework used to model localized neutral or charged excitations in extended materials. Here, the electronic structure of a small cluster is modeled within correlated wavefunction theory, while its coupling to its environment is represented by an embedding potential. We review a number of techniques to represent this background potential, including electrostatic representations and electron density-based methods, and evaluate their application to transition metal oxides.
Leah Isseroff Bendavid, Emily Ann Carter

Quasiparticle Self-Consistent GW Method for the Spectral Properties of Complex Materials

Abstract
The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.
Graphical Abstract
Fabien Bruneval, Matteo Gatti

Gas-Phase Valence-Electron Photoemission Spectroscopy Using Density Functional Theory

Abstract
We present a tutorial overview of the simulation of gas-phase valence-electron photoemission spectra using density functional theory (DFT), emphasizing both fundamental considerations and practical applications, and making appropriate links between the two. We explain how an elementary quantum mechanics view of photoemission couples naturally to a many-body perturbation theory view. We discuss a rigorous approach to photoemission within the framework of time-dependent DFT. Then we focus our attention on ground-state DFT. We clarify the extent to which it can be used to mimic many-body perturbation theory in principle, and then provide a detailed discussion of the accuracy one can and cannot expect in practice with various approximate DFT forms.
Leeor Kronik, Stephan Kümmel

Piecewise Linearity and Spectroscopic Properties from Koopmans-Compliant Functionals

Abstract
Density-functional theory is an extremely powerful and widely used tool for quantum simulations. It reformulates the electronic-structure problem into a functional minimization with respect to the charge density of interacting electrons in an external potential. While exact in principle, it is approximate in practice, and even in its exact form it is meant to reproduce correctly only the total energy and its derivatives, such as forces, phonons, or dielectric properties. Quasiparticle levels are outside the scope of the theory, with the exception of the highest occupied state, since this is given by the derivative of the energy with respect to the number of electrons. A fundamental property of the exact energy functional is that of piecewise linearity at fractional occupations in between integer fillings, but common approximations do not follow such piecewise behavior, leading to a discrepancy between total and partial electron removal energies. Since the former are typically well described, and the latter provide, via Janak’s theorem, orbital energies, this discrepancy leads to a poor comparison between predicted and measured spectroscopic properties. We illustrate here the powerful consequences that arise from imposing the constraint of piecewise linearity to the total energy functional, leading to the emergence of orbital-density-dependent functionals that (1) closely satisfy a generalized Koopmans condition and (2) are able to describe with great accuracy spectroscopic properties.
Graphical Abstract
Ismaila Dabo, Andrea Ferretti, Nicola Marzari

Optical Response of Extended Systems Using Time-Dependent Density Functional Theory

Abstract
In this chapter, time-dependent density functional theory is introduced and an outline of the Runge–Gross theorem is presented. An equation for linear response within time-dependent density functional theory is derived. A key ingredient of this equation is the exchange-correlation kernel for which several modern-day approximation exist. These approximations are investigatead for their ability to capture the excitonic physics in absorption and electron loss spectra. To this end, results for medium (Si and diamond) to large (LiF and Ar) band-gap insulators are presented, which exhibit excitonic physics to varying degrees.
S. Sharma, J. K. Dewhurst, E. K. U. Gross

Spin Excitations in Solids from Many-Body Perturbation Theory

Abstract
Collective spin excitations form a fundamental class of excitations in magnetic materials. As their energy reaches down to only a few meV, they are present at all temperatures and substantially influence the properties of magnetic systems. To study the spin excitations in solids from first principles, we have developed a computational scheme based on many-body perturbation theory within the full-potential linearized augmented plane-wave (FLAPW) method. The main quantity of interest is the dynamical transverse spin susceptibility or magnetic response function, from which magnetic excitations, including single-particle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple-scattering T matrix, which describes the coupling of electrons and holes with different spins. The electron–hole interaction incorporates the screening of the many-body system within the random-phase approximation. To reduce the numerical cost in evaluating the four-point T matrix, we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials. The theory and the implementation are discussed in detail. In particular, we show how the magnetic response function can be evaluated for arbitrary k points. This enables the calculation of smooth dispersion curves, allowing one to study fine details in the k dependence of the spin-wave spectra. We also demonstrate how spatial and time-reversal symmetry can be exploited to accelerate substantially the computation of the four-point quantities. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnet bcc Fe, B2-type tetragonal FeCo, and CrO2 calculated with our scheme. The results are in good agreement with available experimental data.
Christoph Friedrich, Ersoy Şaşıoğlu, Mathias Müller, Arno Schindlmayr, Stefan Blügel

Dynamical Mean Field Theory-Based Electronic Structure Calculations for Correlated Materials

Abstract
We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.
We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.
Silke Biermann

Probing Strongly Correlated Materials in Non-equilibrium: Basic Concepts and Possible Future Trends in First Principle Approaches

Abstract
Time-resolved spectroscopy has an emerging role among modern material-characterization techniques. Two powerful theoretical formalisms for systems out of equilibrium (and thus for time-resolved spectroscopy) are Non-Equilibrium Green’s Functions (NEGF) and Time-Dependent Density Functional Theory (TDDFT). In this chapter, we offer a perspective (with more emphasis on the NEGF) on their current capability to deal with the case of strongly correlated materials. To this end, the NEGF technique is briefly presented, and its use in time-resolved spectroscopy highlighted. We then show how a linear response description is recovered from NEGF real-time dynamics. This is followed by a review of a recent ab initio NEGF treatment and by a short introduction to TDDFT. With these background notions, we turn to the problem of describing strong correlation effects by NEGF and TDDFT. This is done in terms of model Hamiltonians: using simple lattice systems as benchmarks, we illustrate to what extent NEGF and TDDFT can presently describe complex materials out of equilibrium and with strong electronic correlations. Finally, an outlook is given on future trends in NEGF and TDDFT research of interest to time-resolved spectroscopy.
M. Hopjan, C. Verdozzi

Backmatter

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