Fukui function reactivity descriptors

From the Fukui function and hardness to the complete set of shape function reactivity descriptors... 

From the interpretation given to the Fukui function, one can note that the sign of the dual descriptor is very important to characterize the reactivity of a site within a molecule toward a nucleophilic or an electrophilic attack [29,30]. That is, if A/(r) > 0, then the site is favored for a nucleophilic attack, whereas if A/(r) < 0, then the site may be favored for an electrophilic attack. 

Fukui Function and Local Softness as Reactivity Descriptors... 

The use of a dual descriptor defined in terms of the variation of hardness with respect to the external potential, and it is written as the difference between nucleophilic and electrophilic Fukui functions, Equation 12.21, can also be used as an alternative to rationalize the site reactivity [32] ... 

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. 

All of these regioselectivity indicators are called Fukui functions, in honor of Kenichi Fukui, who pioneered the analogous frontier orbital reactivity descriptors in the early 1950s [12-14]. The Fukui function and its twin, the local softness [15]. 

Conceptual density functional theory (DFT) [1-7] has been quite successful in explaining chemical bonding and reactivity through various global and local reactivity descriptors as described in the previous chapters. The Fukui function (FF) [4,5] is an important local reactivity descriptor that is used to describe the relative reactivity of the atomic sites in a molecule. The FF [4,5] is defined as... 

This chapter aims to present the fundamental formal and exact relations between polarizabilities and other DFT descriptors and is organized as follows. For pedagogical reasons, we present first the polarizability responses for simple models in Section 24.2. In particular, we introduce a new concept the dipole atomic hardnesses (Equation 24.20). The relationship between polarizability and chemical reactivity is described in Section 24.3. In this section, we clarify the relationship between the different Fukui functions and the polarizabilities, we introduce new concepts as, for instance, the polarization Fukui function, and the interacting Fukui function and their corresponding hardnesses. The formulation of the local softness for a fragment in a molecule and its relation to polarization is also reviewed in detail. Generalization of the polarizability and chemical responses to an arbitrary perturbation order is summarized in Section 24.4. 

The effect of external field on reactivity descriptors has been of recent interest. Since the basic reactivity descriptors are derivatives of energy and electron density with respect to the number of electrons, the effect of external field on these descriptors can be understood by the perturbative analysis of energy and electron density with respect to number of electrons and external field. Such an analysis has been done by Senet [22] and Fuentealba [23]. Senet discussed perturbation of these quantities with respect to general local external potential. It can be shown that since p(r) = 8E/8vexl, Fukui function can be seen either as a derivative of chemical potential... 

The HF results generated for representative polyatomic molecules have used the /V-derivatives estimated by finite differences, while the -derivatives have been calculated analytically, by standard methods of quantum chemistry. We have examined the effects of the electronic and nuclear relaxations on specific charge sensitivities used in the theory of chemical reactivity, e.g., the hardness, softness, and Fukui function descriptors. New concepts of the GFFs and related softnesses, which include the effects of molecular electronic and/or nuclear relaxations, have also been introduced. 

Introduces and analyzes the usefulness of local reactivity descriptors such as Fukui, shape, and electron localization functions... 

The Fukui function f(r) is a local electronic descriptor of reactivity which finds its origin within density-functional theory (DFT) and is defined as [Parr and Yang, 1989] ... 

On the basis of the foregoing the idea can be used if indeed, knowing a, all properties of a system are determined, including its reactivity descriptors such as hardness, softness, Fukui function and, by combining the last two descriptors, local softness. In this paragraph, an overview will be given on pragmatic steps which can be taken to do so. 

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... 

As opposed to the global reactivity descriptors described above, the analysis of site selectivity in a molecule demands the local descriptors like the Fukui function defined as [35,36],... 

The Fukui functions f(r) are local electronic descriptors of reactivity that find their origin within Density Functional Theory (DPT) and are defined as [Fukui, 1982 Parr and Yang, 1989]... 

Popular qualitative chemical concepts such as electronegativity [1] and hardness [2] have been widely used in understanding various aspects of chemical reactivity. A rigorous theoretical basis for these concepts has been provided by density functional theory (DFT). These reactivity indices are better appreciated in terms of the associated electronic structure principles such as electronegativity equalization principle (EEP), hard-soft acid-base principle, maximum hardness principle, minimum polarizability principle (MPP), etc. Local reactivity descriptors such as density, Fukui function, local softness, etc., have been used successfully in the studies of site selectivity in a molecule. Local variants of the structure principles have also been proposed. The importance of these structure principles in the study of different facets of medicinal chemistry has been highlighted. Because chemical reactions are actually dynamic processes, time-dependent profiles of these reactivity descriptors and the dynamic counterparts of the structure principles have been made use of in order to follow a chemical reaction from start to finish. 

Although information about the overall reaction can be obtained from knowledge of global parameters such as electronegativity and hardness, the reactivity of a particular site of a molecular species can be explained by local quantities such as electron density (p(rj), Fukui function (/(F)) [75], local softness [64], or local hardness [76,77], The dependence of these local quantities on reaction coordinate reflects the usefulness of these quantities in predicting the site selectivity of a chemical reaction. The most important local descriptor is the density p(F) itself, the basic variable of DFT [78], given as ... 

In addition to the various conceptual DFT-based global reactivity descriptors, the local reactivity descriptors also provide valuable insights in determining chemical reactivity patterns. The various local reactivity indices like electron density (p(r)), Fukui function (/(r)), local softness (s(r)), local hardness ( (r)), and philicity (ft)(r)) help to assess the response of a particular atomic site in a molecule during a chemical attack. 

The Fukui function (f(r)) makes an assessment of the tendency towards reactivity of the different local sites of the same molecule and thus serves as an intramolecular reactivity descriptor. The local sofmess (5(r)), on the other hand, compares and correlates the propensity of a pair of interacting molecular neighbors during chemical response and unlike /(r) serves as an intermolecular reactivity descriptor. 

In this connection the usefiilness of local reactivity descriptors for understanding drug metabolism of neonicotinoids, the electrophilic Fukui function of THIAM 6 was investigated (20). 

---