THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 45

the interrelationship between several properties of molecules and their
chemical hardness. To quantify the interaction energy between hard and
soft acids and bases, Ayers relied on the fundamental periodic relationship
between the chemical hardness, size, polarizability, charge, and electro-
negativity of the chemical systems.
The most interesting point to study the physical nature of HSAB is that
it will help us understand why exceptions to the HSAB principle some-
times occur [3].
Pearson [9] invoked the concept of hardness to study the chemical
properties of compounds, specifi cally, the tendency of hard acids to in-
teract with hard bases and the tendency of soft acids to interact with soft
bases. The physical properties of the compounds were not described at that
time [9].
It is not worth mentioning that the physical properties and chemical
properties of acids and bases are interrelated and follow each other.
Thus Ayers [3] commented thus: “Discovering the physical basis of
a chemical principle requires relating the principle to one or more of the
fundamental variational principles that govern chemical reactivity.”
He [3] cited the examples of the electronegativity equalization prin-
ciple [53] and the frontier-electron theory [24] based on the Fukui function
both of them follow directly from the fundamental variational principle for
the electron density.

1.2.20 UNDERSTANDING THE HSAB PRINCIPLE: THE
DOUBLE-EXCHANGE REACTION

The double-exchange reaction between a hard acid-soft base adduct ( A h B s ),
and a soft acid-hard base adduct ( A s B s ) was taken to theorize and under-
stand the HSAB principle. Ayers et al. [69] have explored new approach
based directly on acid- and base-exchange reactions and, especially, the
double-exchange reaction:

A h B s + A s B h ↔ A h B h + A s B s (77)

where A h is a hard acid, B s is a soft base, A s is a soft acid, and B s is a soft
base.