Example from Chemistry

There are three shapes which are particularly important in chemistry and are easily recognized by the number of their faces, all of which consist of equilateral triangles. They are the tetrahedron (four faces), the octahedron (eight faces) and the icosahedron (20 faces). Figure 2.8 contains diagrams of these shapes and examples from chemistry. 

It is gratifying to launch the third edition of our book. Its coming to life testifies about the task it has fulfilled in the service of the community of chemical research and learning. As we noted in the Prefaces to the first and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from chemistry as well as from other fields to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pleasure in addition to learning experience. In our first Preface we paid tribute to two books in particular from which we learned a great deal they have influenced significantly our approach to the subject matter of our book. They are Weyl s classic, Symmetry, and Shubnikov and Koptsik s Symmetry in Science and Art. 

On Whitehead s account, the substance or substratum of classical metaphysics results from a process of translation and transmutation, a procedure of the mind that ought to be recognized as such. If we are to look for substance anywhere, he concludes, I should find it in events which are in some sense the ultimate substance of nature (Whitehead 1920, 19). An example from chemistry helps define what an event is It is a nexus of actual occasions... For example, a molecule is a historic route of actual occasions and such a route is an event (Whitehead 1978, 80).14... 

This book surveys chemistry from the point of view of symmetry. We present many examples from chemistry as well as from other fields, in order to emphasize the unifying nature of the concepts of symmetry. 

An example from chemistry is the use of vesicles, liquids, and foams to direct biomimetic mineralization and polymerization. Such templates, that may only have a transitory existence were used to template the assembly of structurally complex, three-dimensional architectures. Subsequently, within supramolecular chemistry, the term "direeted self-assembly" has become more generally understood to include any templated process that brings together molecular components, even if the directing moiety is part of the final structure. " ... 

An example from chemistry may characterize a typical pattern recognition problem The objects may be chemical compounds and the property to be determined is the presence of a carbonyl group in the molecule. 

This type of reaction occurs at radioactive decay. An example from chemistry is the decay of acetone at high tanperatures ... 

Table 1 Examples from Chemistry for the Application of Multivariate Methods...

Gas-phase reactions play a fundamental role in nature, for example atmospheric chemistry [1, 2, 3, 4 and 5] and interstellar chemistry [6], as well as in many teclmical processes, for example combustion and exliaust fiime cleansing [7, 8 and 9], Apart from such practical aspects the study of gas-phase reactions has provided the basis for our understanding of chemical reaction mechanisms on a microscopic level. The typically small particle densities in the gas phase mean that reactions occur in well defined elementary steps, usually not involving more than three particles. 

Much of the chemistry of diols—compounds that bear two hydroxyl groups—is analo gous to that of alcohols Diols may be prepared for example from compounds that con tain two carbonyl groups using the same reducing agents employed m the preparation of alcohols The following example shows the conversion of a dialdehyde to a diol by... 

The applications of Beer s law for the quantitative analysis of samples in environmental chemistry, clinical chemistry, industrial chemistry and forensic chemistry are numerous. Examples from each of these fields follow. 

Chelation is a feature of much research on the development and mechanism of action of catalysts. For example, enzyme chemistry is aided by the study of reactions of simpler chelates that are models of enzyme reactions. Certain enzymes, coenzymes, and vitamins possess chelate stmctures that must be involved in the mechanism of their action. The activation of many enzymes by metal ions most likely involves chelation, probably bridging the enzyme and substrate through the metal atom. Enzyme inhibition may often result from the formation by the inhibitor of a chelate with a greater stabiUty constant than that of the substrate or the enzyme for a necessary metal ion. 

Espenson gives examples from inorganic chemistry Jencks describes enzyme-catalyzed reactions in which the common intermediate is an acylated enzyme... 

Examples from preparative chemistry indicate the possible occurrence of special alpha-e ects in several other cases. The different reaction of 2- and 4-ethoxy quinolines with a thiol yielding carbostyril and a 4-arylthio derivative, respectively, may indicate the intervention of structures such as 17 in the transition state of the 2-isomer. 

The Hofmann-Loeffler-Freytag reaction has been described with A-chloro-as well as A-bromoamines—the former however usually give better yields. A-chlorinated primary amines react well in the presence of Fe-(II) ions. Just like the Barton reaction, the Hofmann-Loeffler-Freytag reaction has been applied mainly in steroid chemistry. An interesting example from alkaloid chemistry is the synthesis of nicotine 12 by Loeffler ... 

The second main application of the orbital model lies with ab initio calculations in chemistry (Szabo and Ostlund [1982]). The basic problem is to calculate the energy of an atom, for example, from first principles, without recourse to any experimental facts. The procedure consists in solving the time independent Schrodinger for the atom in question, but unfortunately only... 

An interesting example from carbohydrate chemistry is the boron trifluoride-diethyl ether complex catalyzed nucleophilic addition of silyl enol ethers to chiral imines (from n-glyceralde-hyde or D-serinal)22. This reaction yields unsaturated y-butyrolactones with predominantly the D-arabino configuration (and almost complete Cram-type erythro selectivity). 

The composition of I, and possibly its structure, may be deduced by identifying Q. Certain examples from peroxide chemistry will illustrate the scope of the method. The reactions of ferrous(nitriloacetate) and ferrous(ethylenediamine-N,N -diacetate) with hydrogen peroxide are complicated processes.1 A particular scavenger T did indeed divert the reaction at high concentrations of T. The required levels of T were, however, much higher than those that would have been needed to trap the hydroxyl radical, HO. It is thereby ruled out. With this and with spectroscopic evidence, a reactive hypervalent iron complex was suggested as the intermediate. 

The problem of relationship between the activation parameters-the so called isokinetic relationship or compensation law—is of fundamental importance in structural chemistry, organic or inorganic. However, there are few topics in which so many misunderstandings and controversies have arisen as in connection with this problem. A critical review thus seems appropriate at present, in order to help in clarifying ideas and to draw attention to this treatment of kinetic or equilibrium data. The subject has already been reviewed (1-6), but sufficient attention has not been given to the statistical treatment which represents the heaviest problems. In this review, the statistical problems are given the first place. Theoretical corollaries are also dealt with, but no attempt was made to collect all examples from the literature. It is hoped that most of the important... 

When a chemistry space has been defined, a database can be mapped onto the space by assigning each molecule to a cell according to its properties and a diverse subset selected by taking one or more molecules from each cell alternatively, a focused subset can be selected by choosing compounds from a limited number of cells, for example, from the cells adjacent to a cell occupied by a known active. The partitioning scheme is defined independently of... 

Several authors have suggested that the pathway may prove to be the most common mechanism in substitution reactions of octahedral complexes generally. However, the D path can be clearly demonstrated in some cases including at least two examples from Co(III) chemistry. The path (I - III - IV, Fig. 7) through the fivecoordinate intermediate would lead, in the case of rate studies in the presence of excess anionic ligand, to observed first-order rate constants governed by equation (13)... 

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