Fukui function isolated system

The Fukui functions generalize the concept of frontier orbitals by including the relaxation of the orbital upon the net addition or removal of one electron. Because the number of electrons of an isolated system can only change by discrete integer number, the derivative in Equation 24.37 is not properly defined. Only the finite difference approximation of Equation 24.37 allows to define these Fukui functions (noted here by capital letters) F1 (r)... 

As mentioned in [Section 24.1], and as already demonstrated in Equation 24.39, the Fukui functions as well as the chemical hardness of an isolated system can be properly defined without invoking any change in its electron number. We define a new Fukui function called polarization Fukui function, which very much resembles the original formulation of the Fukui function but with a different physical interpretation. Because of space limitation, only a brief presentation is given here. More details will appear in a forthcoming work [33]. One assumes a potential variation <5wext(r), which induces a deformation of the density 8p(r). A normalized polarization Fukui function is defined by... 

Exact Relations between the Different Fukui Functions of an Isolated System... 

In addition to popular finite difference approximations of Fukui functions of an isolated system (Equation 24.38), at least six other different Fukui functions can be defined as responses to a potential. These later concepts do not depend on a net... 

It is shown that Density Functional Theory offers both a conceptual and a computational tool for chemists in relating electronic structure of atoms and molecules to their properties both as isolated systems and upon interaction. The computational performance of DFT in the calculation of typical DFT quantities such as electronegativity and hardness and in the ev uation of atomic electronic affinities and molecular dipole and quadrupole momCTits is assessed. DFT concepts are discussed as such (a non finite difference evaluation of the electronic Fukui function, local softness and its use in similarity analysis of peptideisosteres and the nuclear Fukui function as a indicator of nuclear rearrangemCTits upon reaction) and in the context of principles (EEM, MHP, HSAB) for a variety of reactions involving the influence of solvent on the acidity of alcohols and the addition of HNC to dipolarophiles. 

One of the stumbling blocks in the evaluation of this type of derivatives with respect to the number of electrons N is that the E = E(N) curve for isolated systems (atoms, molecules. ..) shows discontinuities at the integer values of N (the problem of the existence of such a function will be left out (see ref [25] for a discussion in depth) necessitating in the case of the Fukui fbnction and local softness the introduction of right and left hand derivatives f" and f... 

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