THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 46

The electrostatic and electron-transfer contributions to the energy in
the above double-exchange reaction make both the hard acid-hard base
and soft acid-soft base products enormously favorable.
Ayers [3] commented thus: “for this reason, the double exchange reac-
tion should almost always follow the HSAB principle.”
It is now well established [69] that the electron transfer strongly favors
the formation of the soft acid/soft base product, and the electrostatic in-
teraction energies strongly favors the formation of the hard acid/hard base
product.
It was Ayers [3] who opined that the HSAB principle does more than
just make predictions about the double-exchange reaction and the corre-
sponding acid- and the base-exchange reactions and proposed a general
model that includes the electron transfer, the electrostatic effects and also
the polarization effect.

A h B s + A s ↔ A h + A s B s (78)

A h + A s B h ↔ A h + A s B h (79)

B s + A s B h ↔ B h + A s B s (80)

A h B s + B h ↔ B s + A h B h (81)

Equations (78-79) and (80-81) are the corresponding acid-exchange
reactions and the base-exchange reactions respectfully of the double-ex-
change reaction, Eq. (77).
The concept also makes predictions about the behavior of the reactive
sites of the ambidentate ligands and also this leads to the introduction of
the local hard/soft acid/base principle:
An ambidentate base (or acid) tends to bind to soft acids (or bases)
through its soft reactive site and hard acids (or bases) through its hard
reactive site.
Gazquez and Mendez [58] suggested that this rule could be explained
using the local softness [60, 70] which is just the softness multiplied by
the Fukui function:

s + ( r ) = Sf + ( r ) for acids (82)

s − ( r ) = Sf − ( r ) for bases (83)