Fukui function, electrophilic attack

Figure 1. Fukui function/" for attack by an electrophile of chlorpyrifos. Contour levels 0.005 (dark, opaque), 0.001 (light, net), 0.0005 (light, transparent). In the reaction scheme shown on the left-hand side, maxima of the Fukui function are indicated by gray circles.

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. 

Once again, due to the discontinuity of the electron density with respect to N, finite difference approximation leads to three types of Fukui function for a system, namely (l)/+(r) for nucleophilic attack measured by the electron density change following addition of an electron, (2)/ (r) for electrophilic attack measured by the electron density change upon removal of an electron, and (3)/°(r) for radical attack approximated as the average of both previous terms. They are defined as follows ... 

Condensed-to-atom Fukui functions for nucleophilic and electrophilic attacks on H2CO estimated from Equation 12.10 ... 

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],... 

One possible solution of this problem is to differentiate a radical first as electrophilic or nucleophilic with respect to its partner, depending upon its tendency to gain or lose electron. Then the relevant atomic Fukui function (/+ or / ) or softness f.v+ or s ) should be used. Using this approach, regiochemistry of radical addition to heteratom C=X double bond (aldehydes, nitrones, imines, etc.) and heteronuclear ring compounds (such as uracil, thymine, furan, pyridine, etc.) could be explained [34], A more rigorous approach will be to define the Fukui function for radical attack in such a way that it takes care of the inherent nature of a radical and thus differentiates one radical from the other. 

When a molecule accepts electrons, the electrons tend to go to places where/1 (r) is large because it is at these locations that the molecule is most able to stabilize additional electrons. Therefore a molecule is susceptible to nucleophilic attack at sites where/ "(r) is large. Similarly, a molecule is susceptible to electrophilic attack at sites where f (r) is large, because these are the regions where electron removal destabilizes the molecule the least. In chemical density functional theory (DFT), the Fukui functions are the key regioselectivity indicators for electron-transfer controlled reactions. 

FIGURE 18.1 (See color insert following page 302.) Propylene is susceptible to electrophilic attack on the double bond. This can be deduced by plotting (a) the Fukui function from below, / (r), or (b) the HOMO density, pHOMO(r), on the van der Waals surface of the molecule. 

In most cases, the orbital relaxation contribution is negligible and the Fukui function and the FMO reactivity indicators give the same results. For example, the Fukui functions and the FMO densities both predict that electrophilic attack on propylene occurs on the double bond (Figure 18.1) and that nucleophilic attack on BF3 occurs at the Boron center (Figure 18.2). The rare cases where orbital relaxation effects are nonnegligible are precisely the cases where the Fukui functions should be preferred over the FMO reactivity indicators [19-22], In short, while FMO theory is based on orbitals from an independent electron approximation like Hartree-Fock or Kohn-Sham, the Fukui function is based on the true many-electron density. 

In chemistry, one is rarely interested in which point in a molecule is most reactive rather one wishes to identify the atom in a molecule is most likely to react with an attacking electrophile or nucleophiles. This suggests that a coarse-grained atom-by-atom representation of the Fukui function would suffice for chemical purposes. Such a representation is called a condensed reactivity indicator [23]. 

For propylene, the condensed Fukui function not only predicts that the electrophilic attack occurs on one of the doubly bonded carbon atoms, but it also predicts that there is a preference for the terminal carbon, in accordance with Markonikov s rule. Nucleophilic attack is predicted at the boron atom in BF3. 

It is to be noted that/(r) is normalized to unity. Due to discontinuity problem in the number of electrons [13] in atoms and molecules, the right- and left-hand side derivatives at a fixed number of electrons introduces the concepts of EF for nucleophilic and electrophilic attack, respectively. Introducing the finite difference approximation and the concept of atom condensed Fukui function (CFF) [14], the working equations are... 

Continuum model has been applied for the first time to predict the Fukui functions of formaldehyde, methanol, acetone, and formamide in water medium [54], The results reveal that the potential for electrophilic and nucleophilic attack increases when passing from the gas phase to an aqueous medium. The calculated Fukui functions for formaldehyde at Hartree-Fock (HF) level of theory are presented in Table 26.2. 

In this case, the superscript on the derivative indicates that the derivative is taken on the electron-deficient side of the integer NA one can expect that the molecule will readily donate electrons from regions where fA (r) will be large and the derivative can thus be used to probe an electrophilic attack [23,24]. The average of these quantities was introduced as the Fukui function for a neutral (radical) attack [23,24]... 

A Mulliken population analysis was used to estimate the condensed reactivity indexes. In Table 62, the absolute values for the condensed Fukui function for electrophilic attack are shown for the relevant atoms in the heterocyclic compounds. 

Because of the discontinuity of this derivative, a backward Fukui function f"(r) and a forward Fukui function f (r) are defined, corresponding to local descriptors for electrophilic and nucleophilic attack, respectively. In terms of the finite difference approximation, both functions can be written as ... 

If the number of electrons decreases, an electrophilic attack or basic behaviour, electrophilic Fukui function may be related to the HOMO density,... 

The most nucleophilic site at the electron-donor moiety will be the one presenting the highest value of the Fukui function for an electrophilic attack fk, 22 while the most electrophilic site at the electron-acceptor moiety will be the one presenting the... 

Since most of the dienophiles considered are substituted ethylenes, we can take ethylene as a reference to discuss the variations in local reactivity induced by chemical substitution. Ethylene (29) presents a local electrophilicity value tok = 0.37eV at the equivalent carbon atoms Cl and C2. Note that acetylene (32), having equivalent Fukui functions for both electrophilic and nucleophilic attacks, presents a lower electrophilicity pattern as compared with that of ethylene (tok = 0.27 eV at the equivalent carbon centres of structure 29). 

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. 

The issue of regiochemistry can be addressed by identifying sites of local electrophilicity and local nucleophilicity. This was done by calculation of a local electrophilicity index The index of nucleophilicity can be taken as / , the local Fukui function for electrophilic attack. The regiochemistry is then predicted by matching the highest local electrophilicity in the electrophilic component with the largest f for the nucleophilic component. Table 10.10 gives some values of representative dienes and dienophiles. 

This approximation establishes that the strongest bond in a molecule is the one formed by the adjacent atoms with the smallest values of the condensed fukui function, and that the weakest bond is the one formed by the adjacent atoms with the largest values of the condensed fukui function. Note that since the condensed fukui functions are different for nucleophilic, electrophilic, and free radical attacks, the weakest bond in a molecule, which may be associated with the most reactive site (this one may be either of the two atoms forming the bond or the bond itself), may be a different one, depending on the type of attack, in agreement... 

Again the right derivative differs from the left derivative, as indicated by the sign. The maxima of/ indicate regions in the molecule, which prefer attack by a nucleophile, while/ exhibits maxima at sites susceptible to an attack by an electrophile. In other words,indicates where increase of electron density is energetically favorable, while/ is maximal where decrease of electron density is preferred. Practically, the Fukui functions are calculated by finite differences, e.g. ... 

Figure 2. Fukui function/ (r) of parathion for attack by an electrophile.

Figures 1 and 2 show the Fukui functions for electrophilic attack of both compounds. The most prominent maxima / can be easily correlated to the observed metabolic reactions. The phenyl ring of chlorpyrifos shows three side maxima of the Fukui function. The three chlorine substituents occupy exactly these positions, thereby blocking possibly hydroxylation.

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