THEORETICAL METHODOLOGY

The emphasis in this review is on ab initio methodologies, although semiempirical and force-field calculations will be mentioned occasionally. We will concentrate on recent studies which generally use elaborate ab initio methods. Such methods are better suited to tackle, with a reasonable level of confidence, problems where experimental data are scarce and cannot be used to guide and to calibrate the calculations. 

The short section on theoretical methodology that follows is included for the convenience of readers who are not familiar with quantum-mechanics theory, but it does not intend to review the available theoretical methods. The interested reader is referred to the monographs and books listed below. The purpose of this short discussion is to familiarize these readers with some of the common names, abbreviations and jargon used by quantum chemists in the majority of the cited literature and also in this chapter. 

A vast literature which describes and reviews the various quantum-mechanical methods in common use is available, and the reader is referred to these sources for details. Of the rich quantum-mechanics literature we single out a few recent monographs (a) The excellent series on Methods of Electronic Structure Theory edited by Schaefer23, (b) The two-volume monograph Ab Initio Methods in Quantum Chemistry edited by Lawley24. (c) The excellent book by Hehre, Radom, Schleyer and Pople25 that describes in detail 

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Electric-field-driven transport in media made of hydrophilic polymers with nanometer-size pores is of much current interest for applications in separation processes. Recent advances in the synthesis of novel media, in experimental methods to study electrophoresis, and in theoretical methodology to study electrophoretic transport lead to the possibility for improvement of our understanding of the fundamentals of macromolecular transport in gels and gel-like media and to the development of new materials and applications for electric-field-driven macromolecular transport. Specific conclusions concerning electrodiffusive transport in polymer hydrogels include the following. 

To begin we are reminded that the basic theory of kinetic isotope effects (see Chapter 4) is based on the transition state model of reaction kinetics developed in the 1930s by Polanyi, Eyring and others. In spite of its many successes, however, modern theoretical approaches have shown that simple TST is inadequate for the proper description of reaction kinetics and KIE s. In this chapter we describe a more sophisticated approach known as variational transition state theory (VTST). Before continuing it should be pointed out that it is customary in publications in this area to use an assortment of alphabetical symbols (e.g. TST and VTST) as a short hand tool of notation for various theoretical methodologies. 

A number of theoretical methodologies, spanning from high-level ab initio to empirical calculations have been applied to obtain information on the factors that influence the reactivity of Si—H bond towards radicals and atoms. 

Thus it is evident from all these studies that the nature of the C—Li bond varies from compound to compound hence any generalization of the nature of bonding is to be taken cautiously. As Schleyer and Streitwieser have discussed in the past, the C—Li bond is essentially ionic however, the covalent components cannot be neglected . The unnsnal behavior of the C—Li bond has been a subject of discussion from the initial years of applying theoretical methods, and the debate continues in an interesting manner due to the developments of new theoretical methodologies. In fact, we support the implications of Bickelhaupt that there is a covalent contribution to the C—Li bonding, however small this turns out to be in specific examples . 

Improvements of the theoretical methodologies during the past few years have resulted in valuable corrections in the proposed structures. The availability of accurate structural and energetic data has encouraged detailed mechanistic studies of the reactions of organolithium compounds. These are discussed in the next section. 

A proposal for the comprehensive study of chemical processes in a variety of important condensed-phase systems using modern theoretical methodology has been presented. The primary goals of the research are to provide microscopic information on the mechanisms and structural and dynamical properties of the chemical systems proposed for investigation, to test the applicability of modern ab initio molecular dynamics (MD) by comparison with experiment, and to develop and apply novel ab initio MD techniques in simulating complex chemical systems. The proposed research will contribute to the forefront of modern theoretical chemistry and address a number of important technological issues. The PI has carefully attempted to demonstrate his knowledge, ability, and resources to carry out the proposed research projects. 

Differential ionization cross sections, differential in ejected electron energy and emission angle, were the subject of intense study during the 1970s and 1980s. Considerable progress was made in both experimental and theoretical methodologies needed to describe differential cross sections these have been reviewed in IAEA TECDOC-799 [19] and ICRU-... 

The activated dissociation of H2 (D2) on Cu(l 11) and other single crystal Cu surfaces has played a special role in the development of reactive gas-surface dynamics. Early experiments and theory by Cardillo and collaborators [217-219] first demonstrated the power of molecular beam techniques to probe activated adsorption and the theoretical methodology developed by them (6D quasi-classical dynamics on a model PES) only differs from modem treatments in the use of DFT based PES. 

The scope of theoretical methodologies presented in the text reflects my judgment of the degree to which these methodologies impact on a broad range of chemical problems,... 

This part of the review comprises a brief description of the main principles of the various theoretical methodologies that have been used to investigate... 

It is therefore unsurprising that the MD and TST methods used to characterize diffusion processes are also used to simulate sorption. In the theoretical methodologies section that follows, these methods are not mentioned further as they were summarized in the preceding section. Monte Carlo methods are discussed in detail, including a recently developed technique to simulate the location and adsorption of longer chain molecules than would normally be possible by using conventional methods. Furthermore, we present the methodology of a combined MD/Monte Carlo/EM tech-... 

One thus has a theoretical methodology that allows one to compute the rate constant for a chemical reaction directly, without having to solve the com-... 

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