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In deriving the rule of the “equality of the Fukui functions” associated
with chemical reaction, the global HSAB principle was proposed by Pal
et al. [64] as the global softness of acid A ( S A ) was assumed to be equal to
that of the base B ( S B ). Under these conditions, the local softness of atom
k in A is also equal to that of atom l in B, that is
s A k ≈ s B l
(76)
Gazquez and Mendez [58] made remarks that the general statement
of equal local softnesses of the atoms participating in a reaction may be
obtained directly by minimization of the grand canonical potential and
without assuming S A = S B . This is a more general statement of their earlier
defi nition of the local HSAB principle to determine the atoms through
which the reaction between A and B takes place. The principle may also
be viewed as a generalization of the global HSAB principle.
1.2.18 THE FUKUI FUNCTION VERSUS LOCAL HARD-SOFT
CONCEPT
Li and Evans [67] demonstrated that the Fukui function plays a central
role in the study of chemical reactivity and selectivity. Both the frontier
molecular orbital (FMO) theory and the HSAB principle are intrinsically
related to the Fukui function. By using an energy perturbation method
within the framework of DFT, they showed that the FMO theory can be
understood as a part of the HSAB principle. The selectivity of achemical
reaction is determined by the nature of the reaction. Thus, for a hard reac-
tion, the site of minimal Fukui function is preferred; for a soft reaction, the
site of maximal Fukui function is preferred.
Chattaraj [68] made a critical analysis on the local HSAB principle
and frontier orbital theory in order to study of chemical reactivity and site
selectivity. He pointed out that the maximum Fukui function site is the
best for the frontier controlled soft-soft reactions; whereas for the charge
controlled hard-hard interactions, the preferred site is associated with the
maximum net charge and not necessarily the minimum Fukui function.
1.2.19 PHYSICAL BASIS OF THE HSAB PRINCIPLE
The physical basis of HSAB principal was not properly elucidated un-
til the landmark work of Ayers [3]. In this work, Ayers explored
 
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