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. 

We discussed mainly some of the possible applications of Fukui function and local softness in this chapter, and described some practical protocols one needs to follow when applying these parameters to a particular problem. We have avoided the deeper but related discussion about the theoretical development for DFT-based descriptors in recent years. Fukui function and chemical hardness can rigorously be defined through the fundamental variational principle of DFT [37,38]. In this section, we wish to briefly mention some related reactivity concepts, known as electrophilicity index (W), spin-philicity, and spin-donicity. 

Ionization Potential (IP), Electron Affinity (EA), Maximal Charge Acceptance ANmax, and Electrophilicity Index Ground State for the First and Second Row Atoms (Units in eV)... 

Notice that since rj > 0, we always have AE < 0, i.e., the charge transfer process is energetically favorable. We proposed the new density functional theory (DFT) reactivity index, electrophilicity index oj as... 

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.)... 

Since its inception, the concept of electrophilicity index as the theoretical measure of the electrophilic power of an electrophile has attracted considerable interests in the literature. There has been a comprehensive review in Chemical Reviews by Chattaraj et al. [40] specifically on this topic. Only a few recent extensions and developments according to my personal flavor are outlined here. For more information and comprehensive review of the subject, refer to Ref. [40]. 

To describe the electrophilic character of a reactive site within a molecule, a local electrophilicity index [Pg.187]

Besides the applications of the electrophilicity index mentioned in the review article [40], following recent applications and developments have been observed, including relationship between basicity and nucleophilicity [64], 3D-quantitative structure activity analysis [65], Quantitative Structure-Toxicity Relationship (QSTR) [66], redox potential [67,68], Woodward-Hoffmann rules [69], Michael-type reactions [70], Sn2 reactions [71], multiphilic descriptions [72], etc. Molecular systems include silylenes [73], heterocyclohexanones [74], pyrido-di-indoles [65], bipyridine [75], aromatic and heterocyclic sulfonamides [76], substituted nitrenes and phosphi-nidenes [77], first-row transition metal ions [67], triruthenium ring core structures [78], benzhydryl derivatives [79], multivalent superatoms [80], nitrobenzodifuroxan [70], dialkylpyridinium ions [81], dioxins [82], arsenosugars and thioarsenicals [83], dynamic properties of clusters and nanostructures [84], porphyrin compounds [85-87], and so on. 

Along the same line, the CFF for radical attack is defined as the average of fk and. Descriptors such as electrophilicity index and its local counterpart are also a useful quantity [15]. Several other reactivity descriptors have been proposed to explain the reactivity of chemical species [16,17]. 

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. 

An attempt has been made to analyse whether the electrophilicity index is a reliable descriptor of the kinetic behaviour. Relative experimental rates of Friedel-Crafts benzylation, acetylation, and benzoylation reactions were found to correlate well with the corresponding calculated electrophilicity values. In the case of chlorination of various substituted ethylenes and nitration of toluene and chlorobenzene, the correlation was generally poor but somewhat better in the case of the experimental and the calculated activation energies for selected Markovnikov and anti-Markovnikov addition reactions. Reaction electrophilicity, local electrophilicity, and activation hardness were used together to provide a transparent picture of reaction rates and also the orientation of aromatic electrophilic substitution reactions. Ambiguity in the definition of the electrophilicity was highlighted.15... 

Table 7. Estimated chemical hardness (j/), electronic chemical potential (ji), and electrophilicity indexes (

Quantitative relationships have been reported between the global electrophilicity index and the experimental rate coefficients for the reactions of thiolcarbonates and dithio-carbonates with piperidine. The validated scale of electrophilicity was then used to rationalize the reaction mechanisms of these systems. This scale also makes it possible to predict both rate coefficients and Hammett substituent constants for a series of systems that have not been experimentally evaluated to date.48... 

A global electrophilicity index of common benzylating and acylating agents has been established from MO calculations and it shows a quantitative linear correlation with the experimental substrate selectivity index from a series of benzylation and acylation reactions.21 The values of relative rate coefficients predicted from the index may be accurate to within 10%. The reaction of /-butyl chloride with anisole catalysed by /Moluenesulfonic acid in supercritical difluoromethane has been subject to kinetic analysis.22 The proportions of substitution at the ortho -position and disubstitution increase at lower pressures, attributed to the decrease in the hydrogen-bonding ability of the solvent. 

The electrophilicity index for, among others, the parent azete has been tabulated for two different models of the energy-electron number relationships <1999JA1922>. The electrophilicity index in the ground state parabola model and the electrophilicity index in the valance state parabola model tovs are reported as ajgs = tcvs/2 = 1.91. 

Density functional theory (DFT) provides an efficient method to include correlation energy in electronic structure calculations, namely the Kohn-Sham method 1 in addition, it constitutes a solid support to reactivity models.2 DFT framework has been used to formalize empirical reactivity descriptors, such as electronegativity,3 hardness4 and electrophilicity index.5 The frontier orbital theory was generalized by the introduction of Fukui function,6 and new reactivity parameters have also been proposed.7,8 Moreover, relationships between those parameters have been found, and general methods to relate new quantities exist.9... 

This quantity has been identified as an electrophilicity index.5 Note that it is constructed from two important features of an electrophile, electronegativity and charge capacity, which act cooperatively. 

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... 

The global electrophilicity index to, which measures the stabilization in energy when the system acquires an additional electronic charge AN from the environment, has been given the following simple expression 21... 

Electrophilicity index and reaction mechanisms of DA Reactions. Polar cycloaddition reactions... 

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