Fukui bond function

The Fukui bond function has been proposed as a new reactivity index capable of predicting the evolution of breaking and formation of bonds in reactions involving a -conjugated systems... 

Morita Y, Miyazaki E, Umemoto Y, Fukui K, Nakasuji K (2006) Two-dimensional networks of ethylenedithiotetrathiafulvalene derivatives with the hydrogen-bonded functionality of uracil, and channel structure of its tetracyanoquinodimethane complex. J Org Chem 71 5631-5637... 

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. 

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. 

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. 

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 concept was introduced qualitatively in the late 1950s and early 1960s by Pearson, in the framework of his classification of Lewis acids and bases, leading to the introduction of the hard and soft acids and bases (HSAB) principle [19-21]. This principle states that hard acids prefer to bond to hard bases and soft acids to soft bases. In many contributions, the factor of 1/2 is omitted. The inverse of the hardness was introduced as the softness S=l/rj [22]. A third quantity, which can be expressed as a derivative with respect to the number of electrons is the Fukui function, was introduced by Parr and Yang [23,24] ... 

Here, it would be interesting to explore the behavior of acetylenic cation-radicals. Studies of negative Fukui functions for a family of substituted acetylenes showed that removing an electron from the HOMO induces electron rearrangement so that the electron density along the carbon-carbon bond increases. In other words, the electron density in one region of the molecule increases although the total number of electrons decreases (Melin et al. 2007). It must reflect in the reactivity of the acetylenic cation-radicals. 

The relative Michael-acceptor abilities of a variety of substituted aromatic and aliphatic nitroalkenes have been elucidated by computational methods. Several global and local reactivity indices were evaluated with the incorporation of the natural charge obtained from natural bond orbital (NBO) analysis. Natural charges at the carbon atom to the NO2 group and the condensed Fukui functions derived by this method were found to be consistent with the reactivity.187... 

In a study of the reaction of alkynes with hydrogen isocyanide the condensed Fukui function was combined with the overall or global softness to try to rationalize the regioselectivity of attack on the triple bond [153] ... 

To cite some newer work on Fukui functions it was claimed that if one accepts negative values of the function (apparently previously shunned), one can understand reactions in which oxidation of an entire molecule leads to reduction of a part of it (removing electrons from alkynes can increase the electron density in the CC bond) [162] the Fukui functions concept has been extended beyond the local... 

The performance of the method proposed above in the calculation of absolute hardness values of a set of neutral atoms and molecules is investigated. The Fukui indices and the polarization functions for the a-bonds of test molecules are also reported. Finally, the maximum hardness principle was checked by studying the "hardness profile" along the reaction path for the isomerization of HCN and 03H+ systems. 

Among the halide acids the o-bond Fukui function of HF is found to be the smallest. This correlates well with the anomalous behaviour of hydrofluoric acid with respect to the other acids of the series. In fact, HF is a weak acid, whereas the other are strong (e.g. with about the same strength in water solvent). The Fukui indices for HC1, HBr and HI fall almost in the same range. The polarization functions no indicates that o-bond of HF is the less polarizable (0.051 eV), while... 

A full orbital analysis for CO (see Table 4) shows that the ft-bond posses the highest Fukui index (0.62 e V) as well as the highest polarization function (0.118 eV). This agrees with the fact that carbon monoxide works most efficiently as a ft acceptor when interacts with transition metal atoms. 

Fukui functions and local softnesses and their application in typical organic reactions (electrophilic substitutions on aromatic systems, nucleophilic additions to activated carbon-carbon double and triple bonds) [34-39]. 

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... 

It is important to mention that if one makes use of the experimental values of I and A in Eq. (11), to determine the hardnesses in Eq. (39), and one makes use of molecular orbital theory to determine the values of the condensed fukui function, then, if one sets Ng = 1, one finds that this expression provides the correct trends, and reasonable estimates of the bond energies of a wide variety of molecular systems [16]. 

In previous publications, it had already been inferred [8,9,21-26,43], that the larger the fukui function, the greater the reactivity, and this statement had already been successfully used to explain several aspects of the chemical reactivity of different systems. The present approach allows one to understand that this may be due to the fact that the sites with the largest values of the appropriate condensed fukui function may be associated with the weakest bonds, and with those reaction paths with the smallest activation energy barriers. 

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