Electrophilicity local hardness

The pair of electrophilicity and nucleophilicity comes together in chemistry textbooks. Just as the former is formally defined in Equation 13.11, is there a similar, straightforward formalization for the latter It turns out that it is not the case. One of the reasons may lie in the theoretical difficulty in dealing with local hardness [41,42], a quantity that is intrinsically related to nucleophilicity. Another reason stems from... 

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... 

To predict which of the two alkyne carbons, C1 or C2, HNC will preferentially attack, one now invokes the local hard-soft acid-base (HSAB) principle (cf. [157]), which says that interaction is favored between electrophile/nucleophile (or radical/radical) of most nearly equal softness. The HNC carbon softness of 1.215 is closer to the softness of C1 (1.102) than that of C2 (0.453) of the alkyne, so this method predicts that in the reaction scheme above the HNC attacks C1 in preference to C2, i.e. that reaction should occur mainly by the zwitterion A. This kind of analysis worked for -CH3 and -NH2 substituents on the alkyne, but not for -F. 

As emphasized in Section IV of this chapter, the lithiotropy is of much consequence in the reactivity of enolates, the O and C sites competing toward electrophiles. This problem has been examined recently by Meneses and coworkers202, who described a local hardness parameter that can be used as a selectivity index, in particular for a set of ketone lithium enolates. 

Figure 1.12 suggests that for carbonyl complexes the HOMO is localized primarily on the metal centre, with only a modest contribution from oxygen orbitals. Thus by far the majority of reactions of metal carbonyls with electrophiles involve direct attack at the metal, with the carbonyl serving as a spectator ligand. If, however, the metal centre is (i) particularly electron rich and (ii) sterically shielded and the electrophile is hard (in the HSAB sense) and also sterically encumbered, then attack may occur at the oxygen. Thiocarbonyls (LM-CS) are stronger 71-acids than CO and the sulfur is both softer and more nucleophilic. Thus electrophilic attack at the sulfur of thiocarbonyls is more common if the metal centre is electron rich (vcs < 1200 cm-1). Similarly, coordinated isocyanides (CNR) are more prone to attack by electrophiles at nitrogen. This is noteworthy in the sense that free isocyanides are attacked by electrophiles at carbon (Figure 3.19). The resulting carbyne ligands will be discussed in Chapter 5.

Pertrifluoroacetic acid, produced in situ from HP and trifluoroacetic anhydride, is an efficient reagent for B V oxidation of butanone to yield ethyl acetate. The possible mechanism of the oxidation of aliphatic ketones by pertrifluoroacetic acid is discussed. Several organic reactions, including BV oxidations, have been studied by using reactivity and selectivity indexes proposed in the DFT. The concepts of electrophilicity and nucleophilicity have been applied as reactivity descriptors. The local hardness has been applied as well as a selectivity descriptor. The reactivity and selectivity patterns have been studied for the reactants involved in these organic reactions. They have been ranked in theoretical scales, which are comparable with experimental results obtained from... 

Electrophilic additions, Baeyer-Villiger oxidations, and the nucleophilic substitutions have been studied using the density functional theory (DFT), applying the concepts of electrophilicity, nucleophilicity, and the local hardness as reactivity and selectivity descriptors. The reactants have then been ranked in theoretical scales, which proved to be comparable with those obtained experimentally from kinetic data. ... 

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. 

Since biological systems are rich in nucleophiles (DNA, proteins, etc.) the possibility that electrophilic metabolites may become irreversibly bound to cellular macromolecules exists. Electrophiles and nucleophiles are classified as hard or soft depending on the electron density, with hard electrophiles generally having more intense charge localization than soft electrophiles in which the charge is more diffuse. Hard electrophiles tend to react preferentially with hard nucleophiles and soft electrophiles with soft nucleophiles. 

The electronic chemical potential /x, chemical hardness 17, and global electrophilicity 10 for the dipoles 83-86 are displayed in Table 11. Also included in Table 11 are the values of local electrophilicity and the values of the Fukui function for an electrophilic attack and for a nucleophilic attack fk at sites k for these dipoles. The two dipo-larophiles present similar electrophilicity values, 1.52 eV (14) and 1.49 eV (15) (see Table 1). According to the absolute scale of electrophilicity based on the co index,39 these compounds may be classified as strong electrophiles. 

A local version of the electrophilicity can be obtained by multiplying to with the relevant Fukui function. These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa." By means of Koopmans theorem (Section 3.4) the hardness is... 

Geerlings De Proft, 2008 Cardenas et al., 2009 Senet, 1996). One may obtain a condensed-to-atom variant and also for the electrophilic, nucleophilic and radical attacks in the usual way. Moreover, the inverse of tu(r,r ) may generate a hierarchy of nucleophilicity kernel. Unlike the previous formulations, the overall treatment here is general and analytic with hardly any bearing on the explicit form of E(N). The traditional operational definition of local softness and hardness contain the same potential information and they should be interpreted as the local abundance or concentration of their corresponding global properties. 

A similar situation happens with the local electrophilicity. Then, it is necessary to derive new expressions, and conditions that the correct local counterparts of the global softness, hardness, and electrophilicity must fulfill. This work can also be considered as a possible alternative to the traditional expressions of local softness and electrophilicity, see Torrent-Sucarrat et al. (2008, 2010) Gal et al. (2011). 

Conceptual density functional theory has been quite successful in providing quantitative definitions for popular qualitative chemical concepts like electronegativity , hardness and electrophilicity . It has also been found to be useful in providing firm theoretical bases for the associated electronic structure principles. Various global and local reactivity descriptors " have played an important role in analyzing bonding, reactivity, stability, interactions and aromaticity in a variety of many-electron systems as well as a host of their physico-chemical properties. 

In a chemical reaction, a more stable transition state, measured by the magnitude of the activation energy, implies an easier chemical reaction. Aromatic transition states are also known to facilitate the chemical reaction. Zhou and Parr defined the activation hardness as the hardness difference of the products and the transition state and found, in the case of electrophilic aromatic substitution, that the smaller the activation hardness, the faster the reaction is. For this specific reaction they also found a correlation of the activation hardness and Wheland s cation localization energy, also proposed as an indicator of aromaticity. This finding can indeed be interpreted as a manifestation of the maximum hardness principle. A transition state with a high hardness is more stable than one with a smaller hardness and is therefore easier to reach energetically. The same can be said about two transition states with different aromaticity. Again, hardness and aromaticity parallel each other. The activation hardness has been used in numerous applications for the prediction of site selectivity in chemical reac-... 

As noted earlier, the solvent parameters are not independent. Clearly, if a reaction gives rise as a product or as an activated complex to a species that is cationic or has a site with localized positive charge, the reaction will be favored by solvent properties including polarity, polarizability, basicity (whether hard or soft), and by tendencies to covalent or electrostatic interaction with vacant orbitals (i.e., nucleophilicity). Similarly, if the product or activated complex bears a locahzed negative charge, the reaction will still be favored by solvent polarity and polarizabihty, but also by acidity and by the presence in solvent molecules of vacant orbitals capable of receiving electron donation (electrophilicity). 

As a working example, the thiocyanate ion (ACY) may react as a weak electrophilic molecule at its sulfur side and as a strong electrophilic (by reaction electrostatically controlled) by its nitrogen with the Lewis strong acids. Therefore, the electronegativity is actually locally complemented with its companion, the chemical hardness, or with the chemical softness, by the Fukui functions so providing a complete molecular picture of the chemical reactivity, i.e., of the tendency of the complex electronic systems to chemically react. 

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