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Parr and Yang [60] approximated the
f
+
k
and
f
-
k
as follows:
f
+
k
= ρ
LUMO
(
r
)
(69)
and
f
-
k
= ρ
HOMO
(
r
)
(70)
Therefore,
S
+
k
= ρ
LUMO
(
r
) S for nucleophilic attack
(71)
S
-
k
= ρ
HOMO
(
r
) S for electrophilic attack
(72)
The condense softness or the softness of an atom in molecule was de-
fi ned as the sum
K
∑
S
±
=
S
(73)
K
=
1
where
K
is the total number of atoms in the molecule.
The condense hardness or the hardness of an atom in molecule was
given by the following equation:
η
±
= 1/S
±
(74)
According to Fuentealba et al. [61], the condensed Fukui function can
give, in general, valuable information of site selectivity in chemical reac-
tions and systematization in a family of molecules. They have shown the
selectivity toward protonations of anilines, and derivatives molecules can
be correctly assessed by the electrophilic Fukui function. The solvent ef-
fects on the condensed Fukui function are negligible.
Although local hardness and local softness are related, one is not sim-
ply reciprocal of the other. There is a different method for the determina-
tion of the local hardness of atoms in a molecule. This method is based on
the distribution of the electron density at each atom, leading to a net charge
on the atom. The assumption is then made that the local hardness increases
with the net positive charge. As it can be noted from the equations for
the local quantities, the local softness is the measure of the response of
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