Fukui function finite difference method

The Fukui function is approximated by the electron density difference using the finite difference method,... 

The Fukui function defined in Eq. (46) is represented in Fig. 11 for two Na clusters Na4o Naioo- This function was obtained by a finite difference method, that is, using the density of the neutral, positive and negatively charged clusters to perform, at each point f, a parabolic fit of p(f) versus N, from which 0p(r)/0N was then obtained. The densities of Nun, NaJ and Nun come from an extended Thomas-Fermi calculation including the functionals of Eqs. (14), (IS) and (16). 

The HF results generated for representative polyatomic molecules have used the /V-derivatives estimated by finite differences, while the -derivatives have been calculated analytically, by standard methods of quantum chemistry. We have examined the effects of the electronic and nuclear relaxations on specific charge sensitivities used in the theory of chemical reactivity, e.g., the hardness, softness, and Fukui function descriptors. New concepts of the GFFs and related softnesses, which include the effects of molecular electronic and/or nuclear relaxations, have also been introduced. 

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). 

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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