Reactivity of radicals

The rate of the reaction of radical R with substrate S is given by the product of the rate constant and the concentrations (better activities) of the reacting components 

The interactions of various radicals with the same S, under otherwise identical conditions, are not equally rapid. Thus the value of the rate constant is a measure of the reactivity of the radical with the given substrate. According to Arrhenius [12] and the Eyring [13] transition state theory, it holds (in standard notation) that 

The calculation of the rate constant from molecular parameters is based on an estimate of the properties of the hypothetical transition complex. We assume that the structure of the complex forms a transition between the structure of the reacting molecule (or molecules) and the product, but it may be nearer either to the former or to the latter. 

Effects modifying the stability of the transition complex usually also affect the activation energy. Many of these factors, especially the steric effects, also affect AS. In some cases, a certain factor,), can modify the activation energy and AS so that the induced effects counteract each other. At a certain 

It is evident that a calculation of the rate constant neglecting AS will only be correct for a limited number of cases. Series of reactions are known in which AS really remains approximately constant. Other series obey the isokinetic relation in others the change in AS is independent of E [14]. Nevertheless, for the time being, our only choice is to consider only the energy, and compare the result with experiment. A procedure for calculating E at variable AS in a generally applicable form is not yet available. 

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The tendency toward alternation is not the only pattern in terms of which copolymerization can be discussed. The activities of radicals and monomers may also be examined as a source of insight into copolymer formation. The reactivity of radical 1 copolymerizing with monomer 2 is measured by the rate constant kj2. The absolute value of this constant can be determined from copolymerization data (rj) and studies yielding absolute homopolymerization constants (ku) ... 

Entries 4 and 5 point to another important aspect of free-radical reactivity. The data given illustrate that the observed reactivity of the chlorine atom is strongly influenced by the presence of benzene. Evidently, a complex is formed which attenuates the reactivity of the chlorine atom. This is probably a general feature of radical chemistry, but there are relatively few data available on solvent effects on either absolute or relative reactivity of radical intermediates. 

The same high reactivity of radicals that makes possible the alkene polymerization we saw in the previous section also makes it difficult to carry out controlled radical reactions on complex molecules. As a result, there are severe limitations on the usefulness of radical addition reactions in the laboratory. Tn contrast to an electrophilic addition, where reaction occurs once and the reactive cation intermediate is rapidly quenched in the presence of a nucleophile, the reactive intermediate in a radical reaction is not usually quenched, so it reacts again and again in a largely uncontrollable wav. 

Physical Properties and Reactivity of Radicals. By R. Zahradnik AND P. Carsky, Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. 327... 

The extended Hiickel method has been used in a discussion of properties and reactivity of radicals and biradicals (75). We have found it possible to correlate the basicity constants, pKbh. of radical anions with extended Hiickel data (76). 

The chemical reactivity of radicals is governed of course by the same chemical principles as the reactivity of systems having closed-shell ground states. Both equilibrium and rate processes are important here. The paucity of quantitative data on equilibrium and rate constants of radical reactions, suitable from the viewpoint of the present state of the theory, prevents a more rapid development in the MO applications this difficulty, however, is not specific for open-shell systems. 

The fields of combustion and atmospheric chemistry are intimately connected. Both of these fields are dominated by the reactivity of radical intermediates. The oxidation (combustion) of fossil fuels and their derivatives converts chemical energy into heat... 

Before turning to epoxide opening with low valent metal complexes, the reduction of epoxides under Birch conditions [10-13] will be discussed very briefly for historical reasons. The initially formed radical is reduced further to give carbanionic species, that do not display the reactivity of radicals. No C - C bond-forming reactions have initially been reported. 

The overall conclusion from the reaction of BP and 6-substituted BP radical cations with nucleophiles of various strengths is that weak nucleophiles display higher selectivity toward the position of highest charge localization. Thus another important factor in the chemical reactivity of radical cations is represented by the strength of the nucleophile. 

In the light of the success of the Birch conditions for reducing organic compounds it is not surprising that epoxides can be opened by solvated electrons [6-9]. The initially formed radical is then further reduced to give carbanionic species, which do not display the reactivity of radicals. This concept has been extended by Bartmann [10], Cohen et al. [11], Conrow [12], and Yus et al. [13,14] who employed aromatic radical anions as the reduc-... 

A number of approaches based on calculations have been applied in order to obtain information on the factors that influence the reactivity of radical reactions. In particular, for the hydrogen atom transfer [Eq. (15)] the applied methodologies have spanned from high-level ab initio to empirical calculations. 

In the area of stereoselective processes, it is worth mentioning Reaction (7.18) starting from acyclic precursor 13, where the origin of stereoselectivity could be found on the transiency of radicals and their ability of reacting before racemi-zation or conformational changes. This principle is based on the knowledge of lifetime and reactivity of radicals and is called stereoselection at the steady state [29]. 

For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an obvious indicator of reactivity of radicals (in which there is a single unpaired electron). Bonds will be made to centers for which the spin density is greatest. For example, the spin density isosurface for allyl radical suggests that reaction will occur on one of the terminal carbons and not on the central carbon. 

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