Fukui function Kohn-Sham potential

All these functional derivatives are well defined and do not involve any actual derivative relative to the electron number. It is remarkable that the derivatives of the Kohn-Sham chemical potential /rs gives the so-called radical Fukui function [8] either in a frozen orbital approximation or by including the relaxation of the KS band structure. On the other hand, the derivative of the Kohn-Sham HOMO-FUMO gap (defined here as a positive quantity) is the so-called nonlinear Fukui function fir) [26,32,50] also called Fukui difference [51]. 

On the other hand, there is a discrepancy between the predictions of the Kohn-Sham theory of Sect. 2 and of the direct ensemble approach of the present section for the electrophilic and nucleophilic Fukui functions and for the chemical potential. Direct use of the ensemble of Eqs. (28) yields results for f (r), Eq. (34a), and for n, Eq. (30a), which are independent of JT in the range... 

Still another way of using DFT, which does not depend directly on approximate solution of Kohn-Sham equations, is the quantification and clarification of traditional chemical concepts, such as electronegativity [6], hardness, softness, Fukui functions, and other reactivity indices [6, 175], or aromaticity [176]. The true potential of DFT for this kind of investigation is only beginning to be explored, but holds much promise. 

This says that /(r) is the functional derivative (section 7.2.3.2, The Kohn-Sham equations) of the chemical potential with respect to the external potential (i.e. the potential caused by the nuclear framework), at constant electron number and that it is also the derivative of the electron density with respect to electron number at constant external potential. The second equality shows /(r) to be the sensitivity of p(r) to a change in N, at constant geometry. A change in electron density should be primarily electron withdrawal from or addition to the HOMO or LUMO, the frontier orbitals of Fukui [114], hence the name bestowed on the function by Parr and Yang. Since p(r) varies from point to point in a molecule, so does the Fukui function. Parr and Yang argue that a large value of fix) at a site favors reactivity at that site, but to apply the concept to specific reactions they define three Fukui functions ( condensed Fukui functions [80]) ... 

The Kohn-Sham (KS) theory for sybsystems (10,11,14, 15), a direct analog of the corresponding Hartree-Fock approach (16,17), which can be used to define the chemical potential, hardness/softness or the Fukui function (FF) characteristics of reactants (10,11), involves the so called nonadditive kinetic energy functional of the noninteracting system (14), the structure of which is still little understood. Similar nonadditive contributions to the exchange-correlation energy may play a vital role in the DFT treatment of the reactive systems, van der Waals... 

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