Local reactivity indexes Fukui function

These generalized Fukui functions are local reactivity indexes, as they depend on the coordinates r where they are determined, in other words their values vary from one point to another within the molecule. It is clear that these quantities can be used to know how the charge or (and) spin densities respond when there are charge or (and) spin transfer to the reacting molecule. 

Evaluation of the only appropriate Fukui function is required for investigating an intramolecular reaction, as local softness is merely scaling of Fukui function (as shown in Equation 12.7), and does not alter the intramolecular reactivity trend. For this type, one needs to evaluate the proper Fukui functions (/+ or / ) for the different potential sites of the substrate. For example, the Fukui function values for the C and O atoms of H2CO, shown above, predicts that O atom should be the preferred site for an electrophilic attack, whereas C atom will be open to a nucleophilic attack. Atomic Fukui function for electrophilic attack (fc ) for the ring carbon atoms has been used to study the directing ability of substituents in electrophilic substitution reaction of monosubstituted benzene [23]. In some cases, it was shown that relative electrophilicity (f+/f ) or nucleophilicity (/ /f+) indices provide better intramolecular reactivity trend [23]. For example, basicity of substituted anilines could be explained successfully using relative nucleophilicity index ( / /f 1) [23]. Note however that these parameters are not able to differentiate the preferred site of protonation in benzene derivatives, determined from the absolute proton affinities [24],... 

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. 

It can be noted that the local softness is obtained by multiplication of the Fukui function with the global softness the local softness can thus be considered as a weighted distribution of the global softness over the molecule. Due to this fact, the local softness should be used as a intermolecular reactivity index, whereas the Fukui function is an intramolecular reactivity index. The definition of local hardness is less trivial and remains a matter of current debate. 

It is also interesting to examine the effect that the electron-releasing groups may have on the local electrophilicity pattern in ethylene 29. These systems have some importance in the IED processes. Consider for instance the electron-rich ethylenes 33 and 35. On the basis of the Fukui function alone, methyl vinyl ether 33 shows nucleophilic activation at the C2 carbon, fk = 0.470. Dimethylvinylamine 35, on the other hand, displays a similar local reactivity pattern, fk = 0.411. Note that on the basis of the to index, both compounds are predicted as marginally electrophilic. Both compounds 33 and 35 are... 

Besides the global descriptors of reactivity, there are a number of local indices that describe the active sites within a molecnle. Among them, of special interest is the Fukui function [48, 53, 57-60]. This index, besides being a local descriptor of reactivity by itself (i.e., regioselectivity), may act as a convenient distribution function for global quantities. The original definition is as follows [59, 61] ... 

To conclude, we have shown that, despite the complexity of their structural and electronic properties, the reactivity of small metallic clusters can in many cases be understood in simple terms with the use of both global reactivity indexes (ionization potentials, electron affinities, and chemical hardness, which provide a measure of the global cluster reactivity) and local Fukui functions (which allow the identification of special reactive sites within a cluster). All of them can be easily evaluated within the framework of Density Functional Theory. 

TABLE 3 Calculated local reactivity parameters fukui functions (f, C, C), local softness(s, s, s ) and local philicity indexes (co, co, co ) along with the global electrophilicity indices (co) of the mesionic derivatives. 

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