Metallic clusters time-dependent density functional

Banerjee and Harbola [69] have worked out a variation perturbation method within the hydrodynamic approach to the time-dependent density functional theory (TDDFT) in order to evaluate the linear and nonlinear responses of alkali metal clusters. They employed the spherical jellium background model to determine the static and degenerate four-wave mixing (DFWM) y and showed that y evolves almost linearly with the number of atoms in the cluster. 

The photoabsorption spectrum a(co) of a cluster measures the cross-section for electronic excitations induced by an external electromagnetic field oscillating at frequency co. Experimental measurements of a(co) of free clusters in a beam have been reported, most notably for size-selected alkali-metal clusters [4]. Data for size-selected silver aggregates are also available, both for free clusters and for clusters in a frozen argon matrix [94]. The experimental results for the very small species (dimers and trimers) display the variety of excitations that are characteristic of molecular spectra. Beyond these sizes, the spectra are dominated by collective modes, precursors of plasma excitations in the metal. This distinction provides a clear indication of which theoretical method is best suited to analyze the experimental data for the very small systems, standard chemical approaches are required (Cl, coupled clusters), whereas for larger aggregates the many-body perturbation methods developed by the solid-state community provide a computationally more appealing alternative. We briefly sketch two of these approaches, which can be adapted to a DFT framework (1) the random phase approximation (RPA) of Bohm and Pines [95] and the closely related time-dependent density functional theory (TD-DFT) [96], and (2) the GW method of Hedin and Lundqvist [97]. 

Asymmetry of Above-Threshold Ionization of Metal Clusters in Two-Color Laser Fields A Time-Dependent Density-Functional Study. 

In this chapter we will review the recent developments in calculating optical excitations. Thereby, we will revise the key methods that are used to calculate excitation spectra in computational physics putting special emphasis on time-dependent density-functional theory. Moreover, we will discuss several recent applications of these methods to various systems, such as metal clusters, semiconductor nanoparticles, organic and biological molecules. Finally, it will be discussed, how calculated excitation spectra can help in revealing the structure of a specific system. 

This chapter is basically divided into a theoretical part and three sections on applications. We will therefore first review in section 2 several methods which are currently used for calculating the optical excitations and excitation spectra of various systems. Thereby, we will put our focus on time-dependent density-functional theory. Sections 3,4 and 5 review recent applications. Section 3 deals with the excitations in various systems, e.g. metal clusters, semiconductor nanoparticles, and organic or biological systems. Finally, we will discuss the latest findings in two more specific areas section 4 will show, how the calculation of excitation spectra can be used to identify a system s structure, especially applied to clusters and nanoparticles and in section 5 we will briefly introduce a newly proposed scheme for calculating dynamics of excited systems. Finally, in section 6 we conclude. 

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