THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 25

Drago [38] further commented that the equalities, C A = σ A C B = σ B ,
E A = S A , and E B = S B and the statement is made that hardness or softness
isσ A or σ B are incorrect. The consideration of Pearson [9(b)] and Klopman
[24(b)] that hardness and softness are related to the C / E ratio is not always
informative [39]. Further, no simple transformation of E and C parameters
exists, which allows Eq. (6) to produce a set of parameters whose interpre-
tation is consistent with the HSAB equation proposed by Pearson [9],that
is, the correlation, α = σ A , E n = σ B , β = S A , and H = S B have no physical
sense.
Drago [38] opined that “if σ A were a large number for a hard acid and
σ B a large number for a soft base, the product would be large in violation of
the hard prefers hard and soft prefers soft rule. The only way around this
problem is to call one positive and the other negative. If hardness were
negative, stabilization would result from a hard acid and hard base, but
now a destabilization as large as the soft-soft or hard-hard stabilization
would result when a hard acid and a soft base are brought together.”
But this does not make much physical sense in the theoretical explana-
tions of HSAB rule. The claim of Pearson [9] that “even hard substances
have some soft character and vice versa” cannot be accommodated with
the sigma product (σ A σ B ). Further, if hardness is negative and softness is
positive, then intermediate acids and bases must be near to zero; therefore,
σ A σ B would be near zero and there would be practically no hard-hard or
soft-soft contribution to adducts with intermediate acids (or bases) react-
ing with hard or soft bases (or acids). The only remaining possibility that
can be considered for the Eq. (6) is that σ is zero for a hard substance and
appreciable for a soft substance. If σ is zero for a hard acid or base, the
hardness has an important effect.
The HSAB principle is very good in predicting the sign of ΔH correctly,
but not its magnitude. It is not perfect, however, if we try to compare acids
or bases of quite different intrinsic strengths. Steric factors and solvation
energies can also be complicating effects. Thus, Drago and coworkers [40]
modifi ed the four-parameter equation by introducing two new parameters.
They proposed an equation for computing enthalpies of solution-phase
neutral molecule as follows:

- ΔH = C A C B + - E A E B − W (16)

where W is a constant used for an energy always associated with a particu-
lar reactant, such as the enthalpy of dissociation of a dimer allowing it to