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Now, as
χ
= −
μ
Hence,
∆N = (
χ
0
A
−
χ
0
B
)/2(η
A
+ η
B
)
(39)
The corresponding energy change, ∆E was calculated by Pearson as
follows:
∆E = (
E
A
−
E
0
A
) + (
E
B
−
E
0
B
)
= −½(
μ
B
0
−
μ
A
0
)∆N
(40)
Putting
χ
= -
μ
,
∆E = −(
χ
0
A
-
χ
0
B
)
2
/4(η
A
+ η
B
)
(41)
As the acid (A) must be more electronegative than base (B), (
χ
0
A
-
χ
0
B
)
is always positive, and hence an energy lowering results from electron
transfer process.
1.2.12 EXPLANATION OF THE HSAB PRINCIPLE
Equation (41) reveals that the difference in absolute electronegativity
drives the electron transfer, and the sum of the hardness parameter acts
as a drag or resistance. In other words, the differences in electronegativity
drive the electron transfer and the sum of the absolute hardness parameters
inhibits electron transfer.
If both acid and base are soft, (η
A
+η
B
) is a small number; and for a rea-
sonable difference in electronegativities, ∆E is substantial and stabilizing.
This explains the HSAB principle; meanwhile, it seems safe to say that it
explains a part: soft prefers soft.
But, if both acid and base are hard, there is little electron transfer and
energy stabilization from electron transfer, for a given difference in elec-
tronegativities. Parr and Pearson [46] commented “
This result seems para-
doxical
,” and there is the need of the second effect—the formation of the
chemical bond.
Parr and Pearson [46] further pointed out that in the molecule AB, sim-
ilar to the electronegativity (chemical potential) equalization, the ioniza-
tion potential of A,I
A
and the ionization potential B, I
B
are also equalized.
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