Reactivity descriptors

Fukui Function and Local Softness as Reactivity Descriptors... 

In summary, the DFT-based reactivity descriptors are conceptually simple and easy to evaluate. They are useful for studying reactivity, especially in probing... 

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... 

FIGURE 23.5 Profiles of different local reactivity descriptors (electrophilic attack) along the path of the gas phase SN2 substitution F + CH3—Fb —> Fa—CH3 + Fb. Profiles of energy and bond order are also shown. (Reprinted from Chattaraj, P.K. and Roy, D.R., J. Phys. Chem. A, 110, 11401, 2006. With permission.)... 

On the other hand, there is considerable interest to quantify the similarities between different molecules, in particular, in pharmacology [7], For instance, the search for a new drug may include a comparative analysis of an active molecule with a large molecular library by using combinatorial chemistry. A computational comparison based on the similarity of empirical data (structural parameters, molecular surfaces, thermodynamical data, etc.) is often used as a prescreening. Because the DFT reactivity descriptors measure intrinsic properties of a molecular moiety, they are in fact chemical fingerprints of molecules. These descriptors establish a useful scale of similarity between the members of a large molecular family (see in particular Chapter 15) [18-21],... 

The (nonlocal) polarizabilities are important DFT reactivity descriptors. But, how are polarizabilities related to chemistry As stated above, an essential ingredient of the free energy surface is the potential energy surface and, in particular, its gradients. In a classical description of the nuclei, they determine the many possible atomic trajectories. Thanks to Feynman, one knows a very elegant and exact formulation of the force between the atoms namely [22,23]... 

The derivatives of these Kohn-Sham quantities relative to the potentials are other reactivity descriptors ... 

This chapter is intended to provide basic understanding and application of the effect of electric field on the reactivity descriptors. Section 25.2 will focus on the definitions of reactivity descriptors used to understand the chemical reactivity, along with the local hard-soft acid-base (HSAB) semiquantitative model for calculating interaction energy. In Section 25.3, we will discuss specifically the theory behind the effects of external electric field on reactivity descriptors. Some numerical results will be presented in Section 25.4. Along with that in Section 25.5, we would like to discuss the work describing the effect of other perturbation parameters. In Section 25.6, we would present our conclusions and prospects. 

The global reactivity descriptors, such as chemical potential and chemical hardness, are the derivative of energy with respect to the number of electrons. The formal expressions for chemical potential (p.) and chemical hardness (rj) are [1,11]... 

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 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... 

Now, let us try to analyze systematically the behavior of the reactivity descriptors in the presence of electric held. It is always a good idea to start with some simple linear molecules [40] such as HF, HCN, CO, and C2H2 to understand the response of the held on these descriptors. All these calculations were performed by GAMESS software [46] with 6-31G(d,p) basis set and a comparatively weak held range was chosen to vary from 0.000 to 0.012 a.u. In the following, we summarize the results obtained in Refs. [40,41]. 

At this point, it is significant to mention that the direction of the electric held plays an important role in deciding the chemical reactivity of a species (Figure 25.2a through c), i.e., when the held direchon is reversed, the behavior of these descriptors reverses. Moreover, it can be observed that the variation of reactivity descriptors is linear and uniform in this held range. 

Besides, we calculated the field at which the linearity in the variation of reactivity descriptors breaks down and tried to put forward some perturbative... 

In this chapter, we have tried to give an introduction to the response of reactivity descriptors to the external perturbation. We have systematically studied the response... 

SOLVENT EFFECT ON THE CONCEPTUAL DFT-BASED REACTIVITY DESCRIPTORS... 

These descriptors have been widely used for the past 25 years to study chemical reactivity, i.e., the propensity of atoms, molecules, surfaces to interact with one or more reaction partners with formation or rupture of one or more covalent bonds. Kinetic and/or thermodynamic aspects, depending on the (not always obvious and even not univoque) choice of the descriptors were hereby considered. In these studies, the reactivity descriptors were used as such or within the context of some principles of which Sanderson s electronegativity equalization principle [16], Pearson s hard and soft acids and bases (HSAB) principle [17], and the maximum hardness principle [17,18] are the three best known and popular examples. 

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