Reactivity quantitative treatments

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

Reactions involving monocyclic six-membered heteroaromatic rings have not been studied sufficiently extensively to allow a quantitative treatment of substituent effects. However, comparison with aza-naphthalene reactivities indicates that aza- and polyaza-benzene systems must also be highly selective. 

When one compares the brutto polymerization rate constants, a measure of the reactivity of monomers during cationic homopolymerizations is obtained. It was found for p-substituted styrenes that lg kBr increased parallel to the reactivity, which the monomers show versus a constant acceptor 93). The reactivity graduation of the cationic chain ends is apparently overcomed by the structural influence on the monomers during the entire process of the cationic polymerization. The quantitative treatment of the substituent influences with the assistance of the LFE principle leads to the following Hammett-type equations for the brutto polymerization rate constants ... 

A Quantitative Treatment of Reactivity of the Electrophile the Selectivity Relationship... 

The quantitative treatment of the electron-transfer paradigm in Scheme l by FERET (equation (104)) is restricted to the comparative study of a series of structurally related donors (or acceptors). Under these conditions, the reactivity differences due to electronic properties inherent to the donor (or acceptor) are the dominant factors in the charge-transfer assessment, and any differences due to steric effects are considered minor. Such a situation is sufficient to demonstrate the viability of the electron-transfer paradigm to a specific type of donor acceptor behavior (e.g. aromatic substitution, olefin addition, etc.). However, a more general consideration requires that any steric effect be directly addressed. 

It is beyond the scope of this chapter to review the numerous attempts to model 8, 2 reactivity. Besides models describing the reaction qualitatively in terms of valence bond configurations and mostly aiming at interpreting substituent effects, anomalous Bronsted slopes and appearance of intermediates on the reaction pathway (see Pross, 1985 8haik, 1985, and references therein), essentially two types of quantitative treatments have been developed. The more rigorous one, based on ab initio quantum chemical calculations (Berthier et al., 1969 Jorgensen, 1988) has reached quantitative... 

Our intention has been to derive models that can quantify these various effects and thereby build a basis for a quantitative treatment of chemical reactivity. The following simple models that enable calculations to be performed rapidly on large molecules and big data sets have been developed. 

Conclusion. It has been demonstrated that the methods developed for the calculation of physicochemical effects can form the foundation for a general quantitative treatment of chemical reactivity. Based on the factors calculated with these various methods, reactivity functions can be elaborated that are able to assign a numerical reactivity to bonds and combinations of bonds in a molecule. In this manner the course and outcome of organic reactions can be predicted. A quantitative treatment of chemical reactivity is also an essential component in synthesis design since it allows evaluation of the feasibility of various synthetic reactions and pathways. 

Tphe original objectives of this work were to determine how much the relative reactivity of two hydrocarbons toward alkylperoxy radicals, R02, depends on the substituent R—, and whether there are any important abnormalities in co-oxidations of hydrocarbons other than the retardation effect first described by Russell (30). Two papers by Russell and Williamson (31, 32) have since answered the first objective qualitatively, but their work is unsatisfactory quantitatively. The several papers by Howard, Ingold, and co-workers (20, 21, 23, 24, 29) which appeared since this manuscript was first prepared have culminated (24) in a new and excellent method for a quantitative treatment of the first objective. The present paper has therefore been modified to compare, experimentally and theoretically, the different methods of measuring relative reactivities of hydrocarbons in autoxidations. It shows that large deviations from linear rate relations are unusual in oxidations of mixtures of hydrocarbons. 

S. W. (1994) Estimation of chemical reactivity parameters and physical properties of organic molecules using SPARC, in Quantitative Treatments of Solute J Solvent Interactions, Theoretical and Computational Chemistry (eds P. Politzer and J.S. Murray), Elsevier, Amsterdam, pp. 291-353. 

The concepts required for a quantitative treatment of the reactivity of solids were now clear, except for one important issue. According to the foregoing, point defect energies should be on the same order as lattice energies. Since the distribution of point defects in the crystal conforms to Boltzmann statistics, one was able to estimate their concentrations. It was found that the calculated defect concentrations were orders of magnitude too small and therefore could not explain the experimentally observed effects which depended on defect concentrations (e.g., conductivity, excess volume, optical absorption). Jost [W. Jost (1933)] provided the correct solution to this problem. Analogous to the fact that NaCl can be dissolved in H20... 

This section is concerned with the quantitative correlation of reaction rates and equilibria of organic reactions with the structure of the reactants. We will restrict the discussion to benzene derivatives. The focus is on a remarkably simple treatment developed by L. P. Hammett in 1935, which has been tremendously influential. Hammett s correlation covers chemical reactivity, spectroscopy and other physical properties, and even the biological activity of drugs. Virtually all quantitative treatments of reactivity of organic compounds in solution start with the kinds of correlations that are discussed in this section. 

For the quantitative treatment of substituent effects in such reactions, Brown proposed (Brown and Okamoto, 1957) a new Hammett-type structure-reactivity relationship, the Brown equation (1), in terms of substituent constant instead of a in the original Hammett equation. 

On the basis of the above arguments, it appears clear that reactions in micelles can be accelerated by realizing high local concentrations of reactants. Obviously, for opposite reasons reactions can be retarded. This happens, for instance, when only one of the reacting species is transferred into the aggregate. The basic requisite for the occurrence of a reaction, the encounter of the reactants is prevented in this case. Aspects of reactivity in organized assemblies have been reviewed [4-6, 26-29], and this topic continues to attract the interest of several research groups. The analysis of reactivity has also led to quantitative treatments... 

This ion as well as its derivatives have played a key role in the development of current concepts and quantitative treatment of substituent effects on organic reactivity. ... 

The energy required to proceed from reactants to products is AG, the free energy of activation, which is the energy at the transition state relative to the reactants. We develop the theoretical foundation for these ideas about reaction rates in Section 3.2. We first focus attention on the methods for evaluating the inherent thermodynamic stability of representative molecules. In Section 3.3, we consider general concepts that interrelate the thermodynamic and kinetic aspects of reactivity. In Section 3.4, we consider how substituents affect the stability of important intermediates, such as carbocations, carbanions, radicals, and carbonyl addition (tetrahedral) intermediates. In Section 3.5, we examine quantitative treatments of substituent effects. In the final sections of the chapter we consider catalysis and the effect of the solvent medium on reaction rates and mechanisms. 

These differences in reactivity are, depending on the workers concerned, usually attributed to polar effects. Nevertheless, it seems apparent that interpretation is made uncertain by the extreme sensitivity of benzaldehyde oxidation to fortuitous inhibition phenomena. In other words, it is not certain that these rather surprising results cannot be attributed to the quantitative treatment of data from experiments involving considerable difficulties. 

A more quantitative treatment of the olefin reactivity data can be... 

Theoretical quantitative treatments of cycloadditions mainly concern the Diels-Alder reaction. A possible approach is that of calculating the para-localisation energy, that is the variation of Tr-electron energy of the conjugated diene system, when two Tr-electrons are localised upon the atoms, in 1,4-relation to each other, which must form the new tr-bonds. This has been done by Brown , using the molecular orbital method some successful predictions of reactivity and of the positions of addition for polycyclic aromatic hydrocarbons and polyenes were made. This method has also been used by other authors - . 

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