Information-theoretic methods

The first chapter reviews information theoretic methods applied to determination of molecular electronic structure in the context of the Orbital Communication Theory of the chemical bond. The molecule is treated as an information network from which structural information can be obtained. The results of probing molecular charges and bond orders using this method are compared with results obtained by more commonly used means. 

Landon, M.R. and Schaus, S.E. (2006) JEDA joint entropy diversity analysis. An information-theoretic method for choosing diverse and representative subsets from combinatorial libraries. Mol. Div., 10, 333-339. 

Vogt, M. and Bajorath, J. (2007b) Introduction of an information-theoretic method to predict recovery rates of active compormds for Bayesian in silica screening theory and screening trials./, Chem. Inf. Model, 47, 337-341. 

Finally, mention should be made of the development of information theoretic methods for characterizing product energy distributions. Surprisal analysis183 may offer a means of compacting and parametrizing distributions for a wide range of reactions, by comparing with the statistically expected distribution in each case. 

Finally, it is useful to consider what the information-theoretic method predicts when a reagent for an endoergic reaction becomes excited so that... 

The energy disposal from the F + HR reactions has been analyzed by the information-theoretic method using three different models for the prior distribution ... 

Many experimental techniques now provide details of dynamical events on short timescales. Time-dependent theory, such as END, offer the capabilities to obtain information about the details of the transition from initial-to-final states in reactive processes. The assumptions of time-dependent perturbation theory coupled with Fermi s Golden Rule, namely, that there are well-defined (unperturbed) initial and final states and that these are occupied for times, which are long compared to the transition time, no longer necessarily apply. Therefore, truly dynamical methods become very appealing and the results from such theoretical methods can be shown as movies or time lapse photography. 

PDB files were designed for storage of crystal structures and related experimental information on biological macromolecules, primarily proteins, nucleic acids, and their complexes. Over the years the PDB file format was extended to handle results from other experimental (NM.R, cryoelectron microscopy) and theoretical methods... 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

In the first chapter, devoted to thiazole itself, specific emphasis has been given to the structure and mechanistic aspects of the reactivity of the molecule most of the theoretical methods and physical techniques available to date have been applied in the study of thiazole and its derivatives, and the results are discussed in detail The chapter devoted to methods of synthesis is especially detailed and traces the way for the preparation of any monocyclic thiazole derivative. Three chapters concern the non-tautomeric functional derivatives, and two are devoted to amino-, hydroxy- and mercaptothiazoles these chapters constitute the core of the book. All discussion of chemical properties is complemented by tables in which all the known derivatives are inventoried and characterized by their usual physical properties. This information should be of particular value to organic chemists in identifying natural or Synthetic thiazoles. Two brief chapters concern mesoionic thiazoles and selenazoles. Finally, an important chapter is devoted to cyanine dyes derived from thiazolium salts, completing some classical reviews on the subject and discussing recent developments in the studies of the reaction mechanisms involved in their synthesis. 

The mental images, no matter how well grounded scientifically, are individually and collectively biased, as they have been developed after considerable filtering. The filters result from the scientific training of individuals, available supporting information from other processes, existing theoretical methods, limitations of numerical simulation, and characteristics of experimental methods. 

This chapter will try to cover some developments in the theoretical understanding of metal-catalyzed cycloaddition reactions. The reactions to be discussed below are related to the other chapters in this book in an attempt to obtain a coherent picture of the metal-catalyzed reactions discussed. The intention with this chapter is not to go into details of the theoretical methods used for the calculations - the reader must go to the original literature to obtain this information. The examples chosen are related to the different chapters, i.e. this chapter will cover carbo-Diels-Alder, hetero-Diels-Alder and 1,3-dipolar cycloaddition reactions. Each section will start with a description of the reactions considered, based on the frontier molecular orbital approach, in an attempt for the reader to understand the basis molecular orbital concepts for the reaction. 

Only the structures of di- and trisulfane have been determined experimentally. For a number of other sulfanes structural information is available from theoretical calculations using either density functional theory or ab initio molecular orbital theory. In all cases the unbranched chain has been confirmed as the most stable structure but these chains can exist as different ro-tamers and, in some cases, as enantiomers. However, by theoretical methods information about the structures and stabilities of additional isomeric sul-fane molecules with branched sulfur chains and cluster-like structures was obtained which were identified as local minima on the potential energy hypersurface (see later). 

The work described in this paper is an illustration of the potential to be derived from the availability of supercomputers for research in chemistry. The domain of application is the area of new materials which are expected to play a critical role in the future development of molecular electronic and optical devices for information storage and communication. Theoretical simulations of the type presented here lead to detailed understanding of the electronic structure and properties of these systems, information which at times is hard to extract from experimental data or from more approximate theoretical methods. It is clear that the methods of quantum chemistry have reached a point where they constitute tools of semi-quantitative accuracy and have predictive value. Further developments for quantitative accuracy are needed. They involve the application of methods describing electron correlation effects to large molecular systems. The need for supercomputer power to achieve this goal is even more acute. 

On the other hand, not only the enormous number of signals in multicomponent methods but also the large number of species that can be detected in highly resolved spectra and chromatograms, respectively, influence the information amount. Therefore, Matherny and Eckschlager [1996] proposed the introduction of so-called relevancy coefficients, k, into the system of information-theoretical assessment. In analytical practice, the coefficients k can be considered as being weight factors of the information contents of the respective species with which Eq. (9.21) becomes... 

Based on the information flow, a number of information-theoretical performance quantities can be derived, and some important ones are compiled in Table 9.2. The information performance of analytical methods can be related to the information requirement of an given analytical problem. The resulting measures, information efficiency and information profitability, may be used to assess economical aspects of analytical chemistry. 

Although reaction rate expressions and reaction stoichiometry are the experimental data most often used as a basis for the postulation of reaction mechanisms, there are many other experimental techniques that can contribute to the elucidation of these molecular processes. The conscientious investigator of reaction mechanisms will draw on a wide variety of experimental and theoretical methods in his or her research program in an attempt to obtain information about the elementary reactions taking... 

The data collected are subjected to Fourier transformation yielding a peak at the frequency of each sine wave component in the EXAFS. The sine wave frequencies are proportional to the absorber-scatterer (a-s) distance /7IS. Each peak in the display represents a particular shell of atoms. To answer the question of how many of what kind of atom, one must do curve fitting. This requires a reliance on chemical intuition, experience, and adherence to reasonable chemical bond distances expected for the molecule under study. In practice, two methods are used to determine what the back-scattered EXAFS data for a given system should look like. The first, an empirical method, compares the unknown system to known models the second, a theoretical method, calculates the expected behavior of the a-s pair. The empirical method depends on having information on a suitable model, whereas the theoretical method is dependent on having good wave function descriptions of both absorber and scatterer. 

The Ti4+ distribution in TS-1 has also been studied by computational methods (34,62,160-163). The actual location of the Ti atoms in the framework of titanosilicates is difficult to determine experimentally because of the low Ti content (Section II), and information obtained from theoretical methods is, therefore, of considerable interest. In the orthorhombic MFI structure, substitution can take place at 12 crystallographically different tetrahedral (T) sites (T1-T12) (Fig. 1 and Section II.A.l.b). In the monoclinic MFI framework, the mirror symmetry is lost and 24 crystallographically different T sites can be distinguished (Fig. 31) (160). 

Detailed evaluations of connection ductility are usually not performed. However, in some special cases it may be necessary to evaluate moment versus rotation characteristics. Theoretical methods for predicting connection behavior, as well an electronic database of actual test data, are available from Chen 1994. Useful information on moment versus rotation relationships for various types of connections can also be obtained from Committee 43, White 1991, and ASCE Manual 41. 

As discussed in section 2.4.4 the coordinating ability of a solvent will often affect the rate of nucleation and crystal growth differently between two polymorphs. This can be used as an effective means of process control and information on solvent effects can often be obtained from polymorph screening experiments. There are no theoretical methods available at the present time which accurately predict the effect of solvents on nucleation rates in the industrial environment. 

In the last decade, quantum-chemical investigations have become an integral part of modern chemical research. The appearance of chemistry as a purely experimental discipline has been changed by the development of electronic structure methods that are now widely used. This change became possible because contemporary quantum-chemical programs provide reliable data and important information about structures and reactivities of molecules and solids that complement results of experimental studies. Theoretical methods are now available for compounds of all elements of the periodic table, including heavy metals, as reliable procedures for the calculation of relativistic effects and efficient treatments of many-electron systems have been developed [1, 2] For transition metal (TM) compounds, accurate calculations of thermodynamic properties are of particularly great usefulness due to the sparsity of experimental data. 

Despite the fact that the structure of the interface between a metal and an electrolyte solution has been the subject of numerous experimental and theoretical studies since the early days of physical chemistry," our understanding of this important system is still incomplete. One problem has been the unavailability (until recently) of experimental data that can provide direct structural information at the interface. For example, despite the fact that much is known about the structure of the ion s solvation shell from experimental and theoretical studies in bulk electrolyte solutions, " information about the structure of the adsorbed ion solvation shell has been mainly inferred from the measured capacity of the interface. The interface between a metal and an electrolyte solution is also very complex. One needs to consider simultaneously the electronic structure of the metal and the molecular structure of the water and the solvated ions in the inhomogeneous surface region. The availability of more direct experimental information through methods that are sensitive to the microscopic... 

Two sources of mechanistic information, new analytical and new theoretical methods, have surfaced in the past several years. The former class includes new methods in the study of kinetic isotope effects, in NMR spectroscopy, and in X-ray... 

For a long time, this knowledge on carbon-centred radicals has driven the analysis of spectroscopic data obtained for silicon-centred (or silyl) radicals, often erroneously. The principal difference between carbon-centred and silyl radicals arises from the fact that the former can use only 2s and 2p atomic orbitals to accommodate the valence electrons, whereas silyl radicals can use 3s, 3p and 3d. The topic of this section deals mainly with the shape of silyl radicals, which are normally considered to be strongly bent out of the plane (a-type structure 2) [1]. In recent years, it has been shown that a-substituents have had a profound influence on the geometry of silyl radicals and the rationalization of the experimental data is not at all an extrapolation of the knowledge on alkyl radicals. Structural information may be deduced by using chemical, physical or theoretical methods. For better comprehension, this section is divided in subsections describing the results of these methods. 

If appropriate, write the numerical methods subsection ofyour Methods section. Depending on the type and extent of statistical, computational, or theoretical methods used, you may want to create a new subheading (e.g., Statistical Methods or Theoretical Methods) or simply add this information to the end ofyour experimental... 

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