Topological Analysis of the Fukui Function

In this section we present some representative examples to show how the topological analysis of the Fukui function works. Accordingly with the literature [44, 46, 47] the results are commonly reported in two ways the first involves a 3D-representation of/(r) where one isosurface is selected to plot in a way that can represent aU the Fukui basins. Accompanying these isosurfaces are the values of the Fukui function condensed in the corresponding basins. The second way makes it simple to compare with other methods used to condense the Fukui function, due to the fact that all atomic contributions are reported as a single value over each atom k. The geometrical optimization and electronic stmcture calculation have been... 

Fuentealba P, Florez E, Tiznado W (2010) Topological analysis of the Fukui function. J Cheml Theory Comput 6(5) 1470-1478... 

Abstract In this work, the Fukui function will be analyzed using the framework of the topological analysis. First, the Fukui function will be introduced as part of the Density Functional Theory of Chemical Reactivity, and its chemical interpretation will be discussed. Then, some applications showing the importance of the topological analysis will be presented. The applications cover from acids and basis of Lewis, substituted benzenes and as an orientation predictor for the most favorable interaction between clusters (used as building blocks) to form larger stmctures. 

Thus one resorts to contour maps or isosurface plots to represent them. Unfortunately, they show only a part of the information contained in the function, since they depend on the contour (or isosurface) value choice one decides to plot. In order to have a more imambiguous way to analyze a three-dimensional (or higher dimension) function, one could use the framework of the topological analysis. In theoretical chemistiy, this has already been done in the pioneer works of Bader, which originated the Quantum Theory of Atoms in Molecules (QTAIM) [1]. Later this topological analysis was applied to interpret the Electron Localization Function [2-4], and lately it has been applied to the study of the Fukui function [5-7], which is namely the object of this chapter. 

We will start with the presentation of the Fukui function in the framework of the Density Functional Reactivity Theory and its chemical interpretation, [8-14] followed by a brief account of the different ways to analyze it and ending with its topological analysis. Finally, several applications of this analysis will be shown, and some open problems will be discussed. 

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