Reactivity parameters

In the last years, it has been found that the intuitive concepts of electronegativity, hardness, and softness are closely related to basic variables of density functional theory [5]. Thus, through the use of this theory it has been possible to establish expressions that allow one to quantify these concepts, and it has also been possible to demonstrate the principles associated with them. The purpose of the present section is to review some fundamental aspects of density functional theory, and to establish the expressions for several reactivity parameters. 

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A fundament of the quantum chemical standpoint is that structure and reactivity are correlated. When using quantum chemical reactivity parameters for quantifying relationships between structure and reactivity one has the advantage of being able to describe the nature of the structural influences in a direct manner, without empirical assumptions. This is especially valid for the so-called Salem-Klopman equation. It allows the differentiation between the charge and the orbital controlled portions of the interaction between reactants. This was shown by the investigation of the interaction between the Lewis acid with complex counterions 18> (see part 4.4). 

Figure 3. Numerical integration of Equation E2 showing net oxidant [03-N0 ] yields from an initial [NMHCJq = SOOppb. A. Variation with the product reactivity parameter Q here a=)9=l and S=l. B. Variation with the dilution parameter S here a=)9=l, Q=l. When S is small, a nearly stoichiometric yield of oxidant=1000ppb is achieved at higher values of S, oxidant and reactants are diluted with less oxidant accumulation.

There are several systematic nuclear magnetic resonance studies of the interaction between the substituents and the protons and ring atoms of five-membered heterocycles. In some 2-substituted furans, thiophenes, selenophenes, and tellurophenes there is a linear correlation between the electronegativity of the chalcogen and several of the NMR parameters.28 As there also is a good correlation between the shifts of the corresponding protons and carbons in the four heterocycles, the shifts of unknown selenophene and tellurophene derivatives can be predicted when those of thiophene are known. This is of special interest for the tellurophene derivatives, since they are difficult to synthesize. In the selenophene series, where a representative set of substituents can be introduced in the 2- as well as in the 3-position, the correlation between the H and 13C shifts and the reactivity parameters according to Swain and Lupton s two-parameter equation... 

Only in the 3-substituted series could the 77Se shifts be correlated with the reactivity parameters of Swain and Lupton.33... 

Then, it is clear that the functional of the energy could be written in terms of any of the two sets of variables E[p, ps] or E p, p J. Consequently, the nonrelativistic spin-polarized DFT can be developed in both sets of variables p, ps or pT, pL [. In the next section, the set of variables p, ps will be used in the discussion of the reactivity parameters. 

The global parameters help understanding the behavior of a system and lead to applicable and useful principles such as the principle of maximum hardness (MHP) [1], In this chapter, however, our main focus is to introduce the working formula of local reactivity parameters, their actual computations, and practical ways of application to different types of organic reactions. In this process, we mention briefly some of the relevant global reactivity parameters and their calculations as well just to have continuity in the subject matter. 

In order to understand the detailed reaction mechanism such as the regio-selectivity, apart from the global properties, local reactivity parameters are necessary for differentiating the reactive behavior of atoms forming a molecule. The Fukui function [10] if) and local softness [11] t.v) are two of the most commonly used local reactivity parameters. 

These relations highlight the fact that the formalism of DFT-based chemical reactivity built by Parr and coworkers, captures the essence of the pre DFT formulation of reactivity under frontier molecular orbital theory (FMO). Berkowitz showed that similar to FMO, DFT could also explain the orientation or stereoselectivity of a reaction [12]. In addition, DFT-based reactivity parameters are augmented by more global terms expressed in the softness. 

Let us consider an example for the calculation of reactivity parameters of formaldehyde (H2CO) from DFT calculations (Table 12.1). 

The most useful and important application of Fukui function and local softness resides in the interpretation and thereby, prediction of reaction mechanism, especially in the site selectivity or regioselectivity. Since long FMO theory has generally been used to probe the regioselective nature of a reaction, in particular of organic compounds, but the DFT-based local reactivity parameters have emerged as... 

Calculation of the appropriate local reactivity parameters (values for nucleophilic attack for the electrophilic reactant and vice versa)... 

Toropov AA, Kudyshkin VO, VoropaevaNL, Ruban IN, Rashidova S.Sh. (2004c) QSPR modeling of the reactivity parameters of monomers in radical copolymerizations J. Struct. Chem. 45 ... 

The interactions between the components that make up a photopolymer are extremely important in arriving at a working formulation. Here we show that inclusion of pyrrolidone derivatives like NVP or NMP in acrylate systems enhances the ambient cure of a film. From the reactivity parameters of some simple systems we have derived an empirical scheme for the formulation of fully and/or partially reactive systems based on the molar equivalent ratios of the acrylate to pyrrolidone components. The data support the presence of a synergistic effect between NVP and the acrylate components. 

The patterns of reactivity parameters, like the Q-e parameters, can be used to analyze reactivity in both copolymerization and homopolymerization. Look at the data in Table 6-4 and compare with the parameters in Table 6-8. The highly reactive radicals are those with lower values of ns- The highly reactive monomers are those with the more positive or less negative values of v. However, v is not the only consideration, polarity is also important. For example, maleic anhydride is a monomer with one of the most positive v values, but it undergoes facile copolymerization only with monomers with which it has a polarity difference. This is the alternation tendency and is given by... 

Table 21. Comparison of reactivity parameters n, iSn and EF for photocyclizations of pentahelicenes )...

The results obtained in Ref 30 for partially diffusion-controlled recombination show that the field dependence of the recombination rate constant is affected by both the reaction radius R and the reactivity parameter p [cf. Eq. (33)]. Depending on their relative values, the rate constant can be increased or decreased by the electric field. The latter effect predominates at low values of p, where the reactants staying at the encounter distance are forced to separate by the electric field. 

Associated with this is the diffuso-reactive parameter, q, where... 

The selectivity is caused by the electron distribution in the excited diarylethylene. Several reactivity parameters for the photocyclization have appeared to be valuable. The most simple one is the sum of the free valence numbers of the atoms r and s involved in the cyclization in the excited state (E F s) (Fr = /3 — IP, P = bond order)13). The following rules could be derived from a large number of photocyclization reactions 14) ... 

Several reactivity parameters adopted from theoretical chemistry have been used to predict the position at which electrophilic reagents will attack higher aromatics l37). The applicability of such parameters to the non-planar hexahelicene was studied qualitatively in bromination, nitration and acetylation reactions 169), and in a quantitative way in the protiodetritiation of the eight monotritiohexahelicenes 170). 

Table 27. Reactivity Parameters of the Ring Atoms in Hexahelicene Nr (Dewar number), Fr (free valence number), pr (Mulliken overlap population) and Lr (localization energy), Rates of Protiodetritiation Relative to 9-T-Phenanthrene (kre[) and Corresponding Partial Rate Factors (f)...

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. 

Shorter, J Compilation and critical evaluation of structure-reactivity parameters and equations Part 2 , Pure Appl. Chem., 69, 2497-2510(1997). 

Correlations between substituent-induced chemical shift differences and reactivity parameters have been examined. Good linear correlations have been obtained using the Swain-Lupton two-parameter equation ... 

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