THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 42

the electron density to a perturbation in the chemical potential at constant
external potential. Since, the chemical reaction is, in general, considered
as a perturbation in the number of electrons, the local softness can be ef-
fectively used as an appropriate descriptor to probe the chemical reaction.
In particular, this has direct implications to the area of catalysis where the
fl uctuation in charge density is shown to be very important.
It is important to point out the work of Garza and Robles [62] who clar-
ifi ed the defi nition of local hardness within the Kohn-Sham formulation of
the DFT and derived exact equations for the local hardness of open- and
closed-shell electronic systems. They found that the Kohn-Sham indepen-
dent particle kinetic energy does not contribute to local hardness.
It should be noted that the defi nition of local hardness is not very clear
and is defi ned in an ambiguous manner. It has been pointed out by Har-
bola, Chattaraj, and Parr [63] that the derivative is ambiguous for a ground
state due to the Hohenberg-Kohn theorem. Pal et al. [64] observed that
“while the defi nition of local hardness is ambiguous, the local softness
has been defi ned clearly.” Ayers and Parr [30] commented “In the density
functional theory of chemical reactivity, the local hardness is known to
be an ambiguous concept.” Chattaraj et al. [65] gave a critical account on
the present status of the local hardness and analyzed various sources of
confusion and misunderstanding concerning the defi nition and working
equation of local hardness. They analyzed the behavior of hardness-relat-
ed global, local, and nonlocal properties and opined that although local
hardness has become very useful in predicting the region selectivity of
chemical reactions, the lack of a rigorous defi nition in the literature has
shown that different approximations can yield different, and sometimes
contradictory, conclusions.
1.2.17 THE LOCAL HARD-SOFT ACID AND BASE CONCEPT
Parallel to the global developments of the HSAB concept, the concepts of
local softness and hardness have emerged. The local quantities describe
atomic sites in the molecule. Several definitions of the local quantities
have been proposed. Although the definition of local hardness is ambigu-
ous, Ghosh and Berkowitz defined the local softness [66]. The definition
assumes a DFT approach. The local softness has been related to the Fukui
function, which has been associated with the reactivity of the local sites
[60].