Parabolic model addition

Within the framework of the parabolic model, the radical addition... 

Parameters of Various Classes of the Addition of Atoms and Radicals to Multiple Bonds Used in the Parabolic Model [40-45]... 

The polar effect involved in radical addition has been repeatedly discussed in the scientific literature. The parabolic model opens up new prospects for the correct estimation of the polar effect (see Section 6.2.7). It permits one to determine the contribution of this effect to the activation energy using experimental data. This contribution (AE ) is estimated by choosing a reference reaction that involves the same reaction center but in which one or both reactants... 

One can see that the rate constants for the disproportionation of the aminyl and peroxyl radicals involving the C—H bond are substantially lower than the rate constants for the addition of R02 to the aromatic ring of the aminyl radical (k = 3 x 108 L mol-1 s ). Conversely, the reaction of Am with H02 occurs very rapidly and can compete successfully with the addition reaction. Thus, the result obtained within the scope of the parabolic model is in good agreement with the experiment. 

The estimation based on the equations of the parabolic model indicates that a reaction of the type (ArO + H02 —> ArOH + 02) involving phenoxyl radicals also requires no activation energy (in this case, AH> A emin = 57kJ mol-1). However, the addition of the peroxyl radical to the aromatic ring of the phenoxyl radical occurs very rapidly. Hence, the rate constant for this reaction is determined by diffusion processes. The data on the Ee0 values are also consistent with this. For the ArO + HOOR reactions with the O H O reaction center and for Am + HOOR reactions with the N H O reaction center, these values are 45.3 and 39.8 kJ mol-1, respectively [23]. At the same time, the calculation of the preexponential factor in terms of the parabolic model indicates that the rate constant k 7 for the reaction of ROOH with the participation of the aminyl radical is several times higher than that for the reaction involving the phenoxyl radical, where the enthalpies of these reactions... 

In addition, steric parameters, such as volume, surface and refractivity calculated by means of Hyperchem/ Chemplus, were checked. Using a parabolic model a poor correlation with the volume was found wherein the benzyl compound was an outlier. Omitting this compound resulted in a striking correlation (Fig. 6) ... 

Many data sets can be explained much better with the help of this theoretically derived model than with the empirical parabolic model [23, 175, 345]. Only two examples shall be given here, one (eq. 99) describing the spasmolytic activities of mandelic acid esters (Table 14 eqs. 85 and 86), the other one describing the antifungal activities of aliphatic amines vs. Rhinocladium beurmanni (eq. 100) [345] in the latter case the parabolic model gives r = 0.967, while a combination of the parabolic model with an additional, highly interrelated MW term yielded r = 0.994 [344] (chapter 3.7). 

However, the parabolic model is still valuable for structure-activity analyses. It is the simpler model, easier to calculate, and most often a sufficient approximation of the true structure-activity relationship. The calculation of bilinear equations is relatively time-consuming, as compared to the parabolic model strange results may be obtained in ill-conditioned data sets. On the other hand, in many cases the, bilinear model gives a better description of the data, especially if additional physicochemical parameters are included in the regression equation. The lipophilicity optimum of symmetrical curves is precisely described by both, the parabolic model (optimum log P = — b/2a) and the bilinear model (optimum log P = — log P). In the case of unsymmetrical curves the site of the lipophilicity optimum is described much better by the bilinear model (optimum log P = log a — log p — log (b — a) eq. 93) than by the parabolic model. 

Table 7.4. Parameters of various classes of addition of atoms and radicals to multiple bonds used in the parabolic model...

The parabolic model makes it possible to develop an empirical hierarchy of addition reactions. All the known addition reactions are divided a priori into classes in accordance with the atomic structure of the reaction center in the transition state. Each class is characterized by a pair of force constants of the outgoing and incoming bonds or by the parameters b = b and a = b jb( (see above). Subclasses are distinguished in each class. Each subclass is characterized by r = const or br = const, which is confirmed by analysis of a large array of experimental results. Each subclass of reactions can be described additionally by the energy of the thermally neutral reaction eo (see Eq. (7.19) and by the threshold value for which E = 0.5RTprovided that A//e < (see Eq. (7.22). The kinetic parameters for various sub-... 

In Fig. 3, these compositions are compared with their respective CL near band-edge emission energies. Additionally, in Fig. 4, the CL emission peaks are compared with bandgap values obtained by scanning electron microscopy. Using a parabolic model, the following relationship describes the CL peak emission 2 hne emission) (Eq. (1)) as a function aluminum mole fraction for 0 < x < 0.96. 

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