Fukui function computing methods

In these examples, the condensed Fukui functions were computed using Hirsh-feld population analysis [26], which is unique among the commonly employed population analysis methods, because the same results are obtained from the response of molecular fragment and the fragment of molecular response approaches [24]. There are other arguments in favor of the Hirshfeld scheme too [27,28], many of them based on the tendency for the atom-condensed Hirshfeld Fukui functions to be nonnegative [25,29,30]. Nonetheless, condensed Fukui functions maybe computed using any population analysis method common methods... 

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... 

Michelak et al. [45] have computed the Fukui function using a variety of the methods previously described as well as some more sophisticated approximate approaches. Specifically, they considered the finite difference approximation to the derivative with IsN = 1 and AY = 0.01, a modified finite difference formula in which only terms linear in orbital changes and occupation number changes are retained, the frozen core approximation (Eqs. 47, 48) and an approximation to Eq. (46). 

The results of Michelak et al. [45] indicate that while the frontier molecular orbital approximation is sometimes qualitatively different from the other methods of computing the Fukui function, all the other methods usually give qualitatively similar results. Since the Fukui function is used to make qualitative judgements about site reactivity, these results suggest that one may compute the effects of orbital relaxation on the Fukui function in whatever reasonable manner one finds most convenient. 

The Fukui function successfully predicts relative site reactivities for most chemical systems. As such it provides a method for understanding and categorizing chemical reactions. More importantly, the Fukui function can be used to predict what the products of a given reaction will be. As computing the Fukui function becomes faster and easier, its predictive ability might be routinely used to winnow the list of potentially useful reagents, catalysts, etc. before performing the types of experiments or calculations necessary to fully characterize a chemical reaction. This predictive ability renders the Fukui function an important tool of the chemist. 

In 2 computational aspects are discussed, with the assessment of DFT methods ( 2.1) in the evaluation of (a) ionization energies and electron affinities, and via eqn. (11), finite difference estimates of electronegativities and hardnesses ( 2.1.1) Mid (b) of dipole and quadrupole moments ( 2.1.2).In the final paragraph 2.2 a problem at the borderline between computational and conceptual DFT is tackled the evaluation of Fukui fimctions "beyond" the finite difference approximation. In 3 conceptual DFT is discussed, where in 3.1 attention is paid to the evaluation and/or use of DFT based concepts as such the shape factor and the local softness as Molecular Similarity indicators ( 3.1.1), and the nuclear Fukui function ( 3.1.2). In the final part of this Section ( 3.2) the role of DFT based concepts in various principles is discussed. The influence of solvent on the acidity of alkylalcohols is discussed within the framework of Sanderson s Electron ativity Equalization Principle [30] ( 3.2.1). The Hard and Soft Acids and Bases Principle and Pearson s Maximum Hardness Principle [31] are used as the guiding prindples in the study of the cycloaddition reactions of HNC to alkenes and aligmes. 

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