Parr, electrophilicity index

Also, it is interesting to note that in the smooth quadratic interpolation, the curve of the total energy as a function of the number of electrons shows a minimum for some value of N beyond N0 (see Figure 2.1). This point has been associated by Parr et al. [49] with the electrophilicity index that measures the energy change of an electrophile when it becomes saturated with electrons. Together with this global quantity, the philicity concept of Chattaraj et al. [50,51] has been extensively used to study a wide variety of different chemical reactivity problems. 

FIGURE 13.2 Correlation between electrophilicity index and EA of 54 neutral atoms and 55 simple molecules in the ground-state parabola model. (Reprinted from Parr, R.G., Szentpaly, L.V., and Liu, S.B., J. Am. Chem. Soc., 121, 1922, 1999. With permission.)... 

The wide scope of application of the electrophilicity index of Parr, Szentpaly, and Liu has been reviewed.1 Applications to electrophilic aromatic substitutions discussed are few. However, some alkylation and acylation reactions do correlate well with electrophilicity values. In the case of the nitration of toluene and chlorobenzene, correlation is not very good and it is suggested2 that electrophilicity is a kinetic quantity with inherent thermodynamic information. 

From the theoretical point of view, the electrophilicity concept has been recently discussed in terms of global reactivity indexes defined for the ground states of atoms and molecules by Roy et al.18 19. In the context of the conceptual density functional theory (DFT), a global electrophilicity index defined in terms of the electronic chemical potential and the global hardness was proposed by Maynard et al.20 in their study of reactivity of the HIV-1 nucleocapsid protein p7 zinc finger domains. Recently, Parr, Szentp ly and Liu proposed a formal derivation of the electrophilicity, co, from a second-order energy expression developed in terms of the variation in the number of electrons.21... 

Starting from these two quantities, the electrophilicity index (successively defined by Parr and co-workers as ... 

A significant progress was made, when the global electrophilicity was introduced by Parr et al. [29]. Formerly proposed by Maynard [56], the global electrophilicity index was given the following working expression in terms of the fi and t] indices ... 

Another quantity is the electrophilicity index co introduced by Parr... 

The global electrophilicity index (q), introduced by Parr (Parr, et al, 1999) is a useful descriptor of the reactivity that allows a quantitative classification of the global electrophilicity character of a molecule within a unique scale. Current studies based on the DFT and applied to DA reactions, have shown this classification of the diene/ dienophile pair is a powerful tool to predict the feasibility of the process and the type of mechanism involved. This index defined as Eq. 3... 

Owing to the exponential dependence of the rate upon energy, the rate problem reduces mainly to the determination of the lowest energy barrier that has to be surmounted. The ISM model, which was presented in the previous chapter, points, in general terms, to some structural factors that control the barriers of chemical reactions and as a consequence the rate constants. These relevant factors are (i) reaction energy, AEP, AFfi or AG° (ii) the electrophilicity index of Parr, m, a measure of the electron inflow to the reactive bonds at the ttansition state, also characterised as a transition-state bond order (iii) when the potential energy curves for reactants and products can be represented adequately by harmonic oscillators, the relevant strucmral parameters are the force constants of reactive bonds, f and/p in reactants and products, respectively and (iv) equilibrium bond-lengths of reactive bonds, and Zp in reactants and products, respectively. 

For this study, we use our extended database [11] of 47 radical systems, so 12 more than our previously published gas-phase radical electrophilicity scale [1], including C-, N-, O- and S-centered radicals, as well as some halogens, thus comprising a representative set of radicals for applications in organic chemistry. The structures can be retrieved from the Supporting Information. In order to compute the electrophilicity index, Parr s definition was apphed to the solution phase as shown in Eq. 1, using lEF-PCM and—in the case of water—COSMO as the implicit solvation models. Five solvents were chosen, for which the static dielectric constant covers the entire range of nonpolar to polar solvents n-hexane = 1.8819), dichloromethane (Sr — 8.9300), 2-propanol = 19.2640), acetonitrile (Sr = 35.6880) and water = 78.3553). 

Parr et al. [13] have defined an electrophilicity index (to) as follows ... 

Parr et al. [6] defined one more global reactivity descriptor of atoms and molecules. The parameter was labeled as global electrophilicity index, (co). This has special reference to correlate the reactivity of the reference molecules, a drug, with a biomolecule when the reaction becomes either electrophilic or nucleophilic. The proposed ansatz electrophilicity index (co) is defined as... 

Zhou Z, Parr RG. Activation hardness. New index for describing the orientation of electrophilic aromatic substitution. J Am Chem Soc 1990 112 5720-5724. 

Useful information about polarity of de DA processes may be obtained from the difference in the global electrophilicity power of the reactants. This difference has been proposed as a measure of the polar character of the reaction. On the other hand, local reactivity indexes are associated with site selectivity in a chemical reaction. These descriptors should reflect the sites in a molecule where the reactivity pattern stated by the global quantities should take place. For instance, an important local reactivity parameter was introduced by Parr et al., and it was defined as the Fukui fimction (Domingo, et al, 2002)... 

The chemical potential, chemical hardness and softness and reactivity indices have been used by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. The concept of electrophilicity has been known for several decades, although there has not been a rigorous definition of it until recently, Parr et al. [39] proposed a definition did they inspired by the experimental findings of Maynard et al. [40]. The revolution begins, with this simple index which has the ability to connect the major facets of chemical sciences. 

Electrophilicity (Parr et al., 1999), firrther allows coupling of chemical power index with electronegativity to provide the energetic information of... 

One can go further by choosing the first five instead of the first three interaction paths from the data of Table 3.45, because this number is the cardinal of the employed correlation parameters in actual residual-alert-QSARs. However, though electronegativity and chemical hardness are closely related to the total energy, see Eqs. (3.160) and (3.163), using only the first three interacting residual-alert pathways seems appropriate for the present purpose. For future studies, the extra index of electrophilieity (Parr et al., 1999) can be also explicitly incorporated to test its conceptual value in the electrophilic theory of chemical carcinogenesis (Parthasarathi et al., 2004). 

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