Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

Collective electronic excitations at metal surfaces are well known to play a key role in a wide spectrum of science, ranging from physics and materials science to biology. Here we focus on a theoretical description of the many-body dynamical electronic response of solids, which underlines the existence of various collective electronic excitations at metal surfaces, such as the conventional surface plasmon, multipole plasmons and the recently predicted acoustic surface plasmon. We also review existing calculations, experimental measurements and applications.

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Theory of surface plasmons and surface-plasmon polaritons

A density-functional formalism comparable to the theory of Hohenberg, Kohn and Sham is developed for electronic systems subject to time-dependent external fields. The formalism leads to a set of time-dependent Kohn-Sham equations which, in addition to the external potential, contain a time-dependent Hartree term and a local time-dependent exchange-correlation potential. Rigorous properties and explicit approximations of the latter are discussed in detail. Generalizations of the basic formalism to incorporate the nuclear motion and to deal with magnetic effects are described. Within the regime of linear-response theory, the time-dependent Kohn-Sham equations lead to a formally exact representation of the frequency-dependent linear density response. Applications within the linear-response regime include the computation of photoabsorbtion cross sections, the determination of van der Waals forces and the calculation of excitation energies. The latter is based on the fact that the frequency-dependent linear density response has poles at the true excitation energies of the interacting many-body system. The time-dependent Kohn-Sham formalism then leads to a simple additive correction of the Kohn-Sham single-particle excitation energies. Beyond the linear-response regime, the time-dependent Kohn-Sham scheme is applied to atoms in strong femto-second laser pulses to describe multi-photon ionization and harmonic generation in a non-perturbative way.

Density functional theory of time-dependent phenomena

Publisher Summary This chapter provides an overview of the sulfur poisoning of metals. Sulfur apparently bonds so strongly to metal surfaces that marked activity reduction occurs at extremely low gas-phase concentrations of sulfur-containing compounds. In commercial practice, the life of supported metal catalysts may be reduced to only a few months or weeks in the presence of only ppm quantities of sulfur contaminants in the feed. Because of the essentially irreversible adsorption of sulfur compounds on metals, regeneration is usually impossible or impractical. This chapter integrates available information on the interaction of sulfur with metal surfaces with that of poisoning studies to provide a more complete picture of sulfur poisoning and of the mechanism. The chapter stresses the importance of experimental techniques that provide definitive, fundamental information regarding sulfur adsorption and poisoning.

Sulfur Poisoning of Metals

This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.

https://iopscience.iop.org/article/10.1088/0953-8984/27/18/183204/pdf

Nonlocal optical response in metallic nanostructures

The existence of multipole surface-plasmon modes at simple-metal surfaces is demonstrated both experimentally and theoretically. Inelastic reflection electron-scattering experiments on smooth films of K and Na show loss peaks originating from the ordinary surface plasmon as well as from a higher-energy multipole mode. Microscopic density-functional calculations of the electron-loss function reproduce the energy and momentum dispersion of both of these surface modes. For Al, the multipole mode is shown to be too weak to be observable in electron-loss spectroscopy.

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A. Liebsch

Papers

Multipole plasmon modes at a metal surface.

The normal modes at the surface of simple metals

Electronic structure of ordered sulfur overlayers on Ni(001)