Theoretical points

Generalized first-order kinetics have been extensively reviewed in relation to teclmical chemical applications [59] and have been discussed in the context of copolymerization [53]. From a theoretical point of view, the general class of coupled kinetic equation (A3.4.138) and equation (A3.4.139) is important, because it allows for a general closed-fomi solution (in matrix fomi) [49]. Important applications include the Pauli master equation for statistical mechanical systems (in particular gas-phase statistical mechanical kinetics) [48] and the investigation of certain simple reaction systems [49, ]. It is the basis of the many-level treatment of... 

The development of electrostatic precipitators was based mostly on empirical work, and it has produced more than 1000 patents covering all aspects of electrostatic air cleaning. From the theoretical point of view, important milestones were papers published by Deutsch as well as White.These papers deal with the collection efficiency of the electrostatic precipitator. The most important early papers dealing with the electrical charging of particles are the ones published by Arendt and Kallmann, Pautheniet and Moreau-Hanot, and White. ... 

A brief review is given on electronic properties of carbon nanotubes, in particular those in magnetic fields, mainly from a theoretical point of view. The topics include a giant Aharonov-Bohm effect on the band gap and optical absorption spectra, a magnetic-field induced lattice distortion and a magnetisation and susceptibility of ensembles, calculated based on a k p scheme. 

Both from the experimental or theoretical point of view, clusters studies present many difficulties due to their typical size (1-10 nm), usually larger than current systems studied in chemistry, but also too small for many physical standard techniques of characterisation and manipulation. 

From the theoretical point of view, a density functional type theory for systems confined to microporous media is lacking. This seems to be one of the reasons why the problem of crystallization of fluids in disordered media has not been solved so far. Further work in future is needed, however, to solve this and relevant problems. Our expectation is that a combined application of theoretical methods and simulation would provide faster progress in studies of fluids and mixtures in microporous media. At present, the models studied in theory and simulations are quite far from the systems of experimental focus. Hopefully, favorable changes will occur in future. 

In some cases, e.g., the Hg/NaF q interface, Q is charge dependent but concentration independent. Then it is said that there is no specific ionic adsorption. In order to interpret the charge dependence of Q a standard explanation consists in assuming that Q is related to the existence of a solvent monolayer in contact with the wall [16]. From a theoretical point of view this monolayer is postulated as a subsystem coupled with the metal and the solution via electrostatic and non-electrostatic interactions. The specific shape of Q versus a results from the competition between these interactions and the interactions between solvent molecules in the mono-layer. This description of the electrical double layer has been revisited by... 

The 8-aza analogs of purine bases were the first to be studied among all the aza analogs of nucleic acid bases (as early as 1945). Before that time the chemistry of these substances had not been treated in detail from any aspect. Thus the entire chemistry of the u-triazolo [4,5-d]pyrimidines was developed only in connection with the study of antimetabolites of nucleic acid components. Therefore all the papers involved are largely of preparative character and only rarely discuss. theoretical points. 

Compared with very intensive work in the development of metal-catalyzed cycloaddition reactions, the work in the field of understanding these reaction from a theoretical point of view is very limited. Although there are many reasons for this, the main reason is probably that only recently has it become possible to perform trustworthy calculations for metal systems to obtain reliable information about reaction courses for metal-catalyzed cycloaddition reactions. 

Yamamoto et al. have developed a catalytic enantioselective carbo-Diels-Alder reaction of acetylenic aldehydes 7 with dienes catalyzed by chiral boron complexes (Fig. 8.10) [23]. This carbo-Diels-Alder reaction proceeds with up to 95% ee and high yield of 8 using the BLA catalyst. The reaction was also investigated from a theoretical point of view using ab-initio calculations at a RHF/6-31G basis set. 

We are now able to understand the Lewis acid-catalyzed normal electron-demand carbo-Diels-Alder reaction from a theoretical point of view. The calculated influence of the Lewis acids on the reaction rate, regio- and stereoselectivity in an... 

The mechanism for the hetero-Diels-Alder reaction of benzaldehyde 9 with the very reactive diene, Danishefsky s diene 10, catalyzed by aluminum complexes has been investigated from a theoretical point of view using semi-empirical calculations [27]. The focus in this investigation was to address the question if the reaction proceeds directly to the hetero-Diels-Alder adduct 11, or if 11 is formed via a Mukaiyama aldol intermediate (Scheme 8.4) (see the chapter dealing with hetero-Diels-Alder reactions of carbonyl compounds). 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

From a theoretical point of view the study of the kinetics of coupled catalytic reactions makes it possible to investigate mutual influencing of single reactions and the occurrence of some phenomena unknown in the kinetics of complex reactions in the homogeneous phase. This approach can yield additional information about interactions between the reactants and the surface of the solid catalyst. 

Oxalic Acid, Salts of, Bertholet (Ref 2) in 1883 noticed that some salts of oxalic add, eg mercuric or silver, have the properties of primary expls. According to Urbadski (Ref 14), although they have no practical application as initiators, it is interesting from a theoretical point of view, due chiefly to the fact that the general equation for the decompn of oxalates... 

Brisance and power are quantities that can be defined more exactly than sensitivity, and PETN is one of the most powerful and brisant expls known. It is also among the most studied expls, from both exptl and theoretical points of view. In this section we will consider PETN s steady detonation parameters, thermochemistry, and initiation characteristics,... 

Among the organic reactions that have been investigated in aqueous medium, the Diels-Alder cycloaddition has been the most studied owing to its great importance from the synthetic and theoretical point of view [7a, bj. In this section Diels-Alder reactions carried out in water under conventional conditions of temperature and pressure will be illustrated. The use of water at supercritical or near-supercritical conditions will be discussed in Section 6.4. 

In order for an experimental test of the kinetic behaviour to be as informative as possible, the system investigated should fulfil various specific requirements. From the experimental point of view, the reaction should cause a minimum of change in the reaction medium and be without side-reactions as far as possible, in order for accurate and well-defined rate measurements to be feasible. For the same reason an accOTate physical method which can be applied without distiubing the reacting system is to be preferred. From the theoretical point of view, it is desirable that the steric effects play as important a role in the reaction as possible, because only then is a sizeable effect to be expected. Finally, a transition state of well-known conformation is a necessary prerequisite for the quantitative application of the theory. 

The functional groups outlined in Fig. 10 are all bifunctional ligands that can, at least from a theoretical point of view, form monomeric, dimeric, or oligomeric complexes with metal ions or a diorganoboryl group. 

Probably the most basic information about a material that we need to know is its strength. But what precisely do we mean by the term strength In practice, the answer that engineers give to this question is to define the strength of a material as the force experienced at the point where it fractures. This topic is one that is complex from a theoretical point of view, largely because fracture is a point of discontinuity, and hence cannot readily be interpreted in terms of events leading up to it. 

In recent times, the study of molecular non-rigidity has been characterized by new and important developments in both experimental and theoretical directions. From the theoretical point of view, the pioneer work of Longuet-Higgins initiated numerous further studies The aim of this work was to extend the concept of symmetry to non-rigid molecules undergoing certain internal movements, the so-called feasible transformations. Some recent discussion of these problems may be found in Refs. for example. 

More concretely, the aim of our investigation is to examine, from a theoretical point of view, the relation between the non-rigidity of pentacoordinate molecules and the characteristics of the temporal evolution of systems of such molecules towards chemical equilibrium. We also want to indicate the type of experimental information needed concerning the time evolution of these systems, in order to sharpen our ideas on the feasibility of the internal movements. We here give an account of the main aspects of our attempt and try to present it in a unified and synthesizing fashion. 

The important role of radicals and radical ions in various branches of chemistry (e.g., electrochemistry, radiation chemistry, macromolecular chemistry), their remarkable physical properties and reactivity, as well as the specific problems in a quantum chemical approach, make this region interesting from the theoretical point of view. 

Optical spectra of radicals are interesting from the theoretical point of view because the first band or even several bands even with small systems are frequently located in the visible region. With many systems, the process of electron-shell opening is connected with a considerable red shift of the first (longest wavelength) band, this shift being sometimes of several eV. 

The quantities boo and Soo represent the solution of the problem of drawing parallel lines through the given set of points by the method of least squares. They are obtained relatively easily and can serve to check the whole calculation. The function Sx = f(x) always has a minimum however, the conditions have not been explored when it has only one minimum. This case would be important from the theoretical point of view however, in practice there is no real danger... 

Noble metal nanoparticles dispersed in insulating matrices have attracted the interest of many researchers fromboth applied and theoretical points of view [34]. The incorporation of metallic nanoparticles into easily processable polymer matrices offers a pathway for better exploitation of their characteristic optical, electronic and catalytic properties. On the other hand, the host polymers can influence the growth and spatial arrangement of the nanoparticles during the in situ synthesis, which makes them convenient templates for the preparation of nanoparticles of different morphologies. Furthermore, by selecting the polymer with certain favorable properties such as biocompatibiHty [35], conductivity [36] or photoluminescence [37], it is possible to obtain the nanocomposite materials for various technological purposes. 

The fact that in HPLC only UV-active components are registered, whereas in titration all basic functional groups are detected constitutes a difference in specificity (quality) and sensitivity (quantity) of these two methods relative to a given impurity. See Fig. 4.17 (left). [Solvent A (water) behaves differently from the other four as can be seen from Fig. 4.17 (right). The material was known to exist in a crystal modification that theoretically contains 3.2% water, and moderate drying will most likely drive off only the excess Indeed, the best-dried batches are all close to the theoretical point (circle, arrow in Figs. 4.16-17), and not near zero. This is only partly reflected in Table 4.15, column A for this reason tabular and graphic information has to be combined. Solvent B, which is an alcohol, behaves more like water... 

The study of molecular systems containing metal atoms, particularly transition metal atoms, is more challenging than first-row chemistry from both an experimental and theoretical point of view. Therefore, we have systematically studied (3-5) the computational requirements for obtaining accurate spectroscopic constants for diatomic and triatomic systems containing the first- and second-row transition metals. Our goal has been to understand the diversity of mechanisms by which transition metals bond and to aid in the interpretation of experimental observations. 

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