THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 43

Apart from the celebrated HSAB principle, one more principle was
proposed by Pal and his coworkers [64] to describe the hard-soft behavior
of the atomic sites in the molecule is the local HSAB concept.
The fact that the reactivity of the different sites of a molecule toward
electrophilic and nucleophilic attacks is not the same can be correlated
through the corresponding electrophilic and nucleophilic defi nitions of
local softness. In particular, the condensed defi nitions based on fi nite
difference approximation of obtaining the derivatives have now been
conveniently used. In general, it has been shown that for any individual
molecule, the most reactive site is located at the atom with the largest
value of local softness of Fukui function. However, Gazquez and Mendez
have shown that the interaction between two molecules will not necessar-
ily occur through their softest atoms but rather through those atoms whose
Fukui functions are the same. This version of the local HSAB principle
was proved by the minimization of the grand canonical potential. Assum-
ing the global softnesses of the molecules to be similar, the local HSAB
principle states that the local softnesses of the interacting atoms are same.
It is interesting to investigate if the equality of local softnesses of the in-
teracting atoms is a more general principle, that is, whether this holds even
when the global softnesses of the two molecules have different values.
For a polyatomic system, the local softness s ( r ) ( s is the global soft-
ness) is proportional to the Fukui function f ( r ) [11]. This function repre-
sents the sensitivity of the chemical potential of a system to an external
perturbation applied locally, such as a magnetic or an electrostatic fi eld. In
this case, the HSAB principle is locally applied: “hard regions of a system
prefer to interact with hard reagents whereas soft regions prefer soft spe-
cies.” In a chemical reaction, the most effi cient interaction will be between
the softest parts of each molecule. This allows the transfer of maximum
electron from a base to an acid.
Gazquez and Mendez [58] showed that the energy of stabilization be-
tween the two reacting systems A and B is greater if the Fukui functions of
the reacting atoms in A and in B are greater. However, they also showed
that the interaction between A and B does not necessarily occur through
the softest atoms of A and B, but through those atoms whose Fukui func-
tions are roughly close to each other. That is,

f k (A) ≈ f l (B) (75)