THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 22

Here, it is important to mention the work of Berkowitz [32] who in
1987 obtained an expression for the amount of charge transfer for the de-
scription of the initial stages of the reaction between a Lewis acid, A and a
Lewis base, B using the density functional theory (DFT) [10−11].
He showed that for the soft acid-soft base interaction, the amount of
charge transfer is controlled by the frontier orbitals. Thus, the exclusive
role that frontier orbitals play in chemical reactivity was confi rmed by his
work.

1.2.9 THE FOUR-PARAMETER EQUATION AND ITS
MODIFICATIONS

The order of the strength of a series of Lewis acids and/or bases may vary
with the variation of the Lewis acid and/or base, which is used to rank the
strength of the Lewis acids and/or bases. Thus, the donor and acceptor
properties of acids and bases are interrelated [33]. In an attempt to cor-
relate the magnitude of the donor-acceptor interactions with electronic
properties of the acids and bases, Drago and his coworkers [34] in 1965
proposed an empirical equation that is popularized as “four-parameter
equation” or double-scale equation. Recognizing the interdependence of
the donor and acceptor properties of acids and bases, they represented the
enthalpy of interaction of donor-acceptor pairs in a poor solvating media
as follows:

-ΔH = E A E B + C A C B (10)

Here, A and B represent the electron acceptor and donor, respectively,
while E (“electrostatic”) and C (“covalent”) are empirically determined
parameters. This relationship provides a useful means of predicting en-
thalpies for the formation of donor-acceptor complexes for which the ex-
perimental values are not available.
It relates the hard-soft principle as follows:
“For there to be a strong donor-acceptor interaction, the two molecules
must match in the sense that both must have a large E parameter or a large
C.”

It goes beyond the hard-soft principle in that the E and C parameters
are not exclusive so that both the E and C parameters for a given molecule
might be either large or small.