Theoretical Approach and Methods

In this section, we discuss theoretical methods, which can be applied for calculations of photoabsorption and PL spectra of silica and germania nanoparticles. We start with the choice of model cluster simulating these materials and point defects in them and consider methods for geometry optimization in the ground and excited electronic states (Subsection 2.1). This is followed by the description of more advanced quantum chemical methods for accurate calculations of excitation energies (Subsection 2.2) and the section is completed by the discussion on the theoretical procedure used for predicting vibronic spectra associated with point defects (Subsection 2.3). 

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The velocity of elastic ultrasonic waves in solution is strongly influenced by solute-solvent and solute-solute interactions which are determined by the chemical structure of the solute and solvent molecules. Still, acoustical methods have made only minor contributions to the detailed description of solute-solvent interactions. Ultrasonic velocity measurements are mostly limited to obtaining hydration numbers of molecules in aqueous solution [Br 75]. The successful application of acoustical methods to physico-chemical investigation of solutions became possible after development of adequate theoretical approaches and methods for precise ultrasonic velocity measurements in small volumes of liquids [Sa 77, Bu 79]. 

The Schrodinger equation can also be solved semi-empirically, with much less computational effort than ab initio methods. Prominent semi-empirical methods include MNDO, AMI, and PM3 (Dewar 1977 Dewar etal. 1985 Stewart 1989a Stewart 1989b). The relative computational simplicity of these methods is accompanied, however, by a substantial loss of accuracy (Scott and Radom 1996), which has limited their use in geochemical simulations. Historically, semi-empirical calculations have also been limited by the elements that could be modeled, excluding many transition elements, for example. Semi-empirical calculations have been used to predict Si, S, and Cl isotopic fractionations in molecules (Hanschmaim 1984), and these results are in qualitative agreement with other theoretical approaches and experimental results. 

Since a topological analysis of electric density is available, first we snmmarize briefly various theoretical approaches and terms nsed in these approaches [2] (experimental methods are considered in Chapter 4). 

Electronic and optical properties of complex systems are now accessible thanks to the impressive development of theoretical approaches and of computer power. Surfaces, nanostructures, and even biological systems can now be studied within ab-initio methods [53,54]. In principle within the Born-Oppenheimer approximation to decouple the ionic and electronic dynamics, the equation that governs the physics of all those systems is the many-body equation ... 

The rapid growth of ab initio quantum mechanical (QM) simulations of condensed matter means that a comprehensive review of theoretical approaches and applications would in itself occupy a book. In this chapter the emphasis will be placed on QM studies of silicate and oxide systems. The key technologies will be identified and a critique of the possibilities and inadequacies of current theory presented. Although we discuss the technical details of implementation of QM methods, and some fundamental issues with regard to the description of electron interactions, the intention is to provide a general reference for non-experts in this field. Recent work based on semi-empirical approaches to QM simulations will not be reviewed (e.g. LaFemina, 1992 Goniakowski etal., 1993). 

Without delving deeply into the workings of any specific method, we will try to convey both the capabilities and the limitations of present theoretical approaches, and to point out directions for future progress. 

This chapter introduces in a tutorial manner some numerical methods for solving mass transport equations for specific electrochemical systems. These are applied to polymer coatings on electrode surfaces containing redox species. Unlike some theoretical approaches, numerical methods are considerably more straightforward and require only some knowledge of programming. For a typical mass transport situation, the equation to be solved is... 

In this chapter, methods are discussed for the characterization of the chemical structure, the morphology, and the thermal properties of SMPs. Methods for quantification of the macroscopic SME are described in detail for dual-shape and tripleshape polymer systems with thermally-induced SME as well as polymer-systems with photo-induced or magnetically-induced SME. Finally, application-oriented testing of SMPs and also theoretical approaches and computational methods for simulating the SME are described. 

We give here a description of the practicalities to consider if one undertakes the computation of vibrational circular dichroism intensities. Some of these will be general for any of the theoretical approaches, and some will be specific for the VCT method which we have implemented at the ab initio level. 

Cuny et al. have presented results of first-principles calculations of quadrupolar parameters measured by solid-state NMR spectroscopy. Different computational methods based on density functional theory were used to calculate the quadrupolar parameters. Through a series of illustrations from different areas of solid state inorganic chemistry, it is shown how quadrupolar solid-state NMR properties can be tackled by a theoretical approach and can yield structural information. 

The English translation of this book by D. Smith and N. G. Adams provides a detailed account of theoretical approaches and experimental techniques of adsorption. The subject matter, essentially comprising physical chemistry, includes defined substances, defined surfaces and their preparation, methods for studying the texture of adsorbents, methods of studying adsorption, the surface structure of solids, theories of adsorption forces, adsorption kinetics and thermodynamics, theories of adsorption equilibria, the mechanisms of physical adsorption and chemisorption, adsorption from flowing gases and liquids, practical applications of adsorption, adsorption from solutions and the relationship between adsorption and catalysis. 

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