648
Bioinorganic Chemistry
the hard and soft classiFcation scheme. In
another example, in the iron–sulfur pro-
tein rubredoxin, sulfur exclusively (soft)
coordinates to both ±e
2
+
(borderline) and
±e
3
+
(hard).
8.6
Conclusions
Note again that the numerical values
associated with hardness–softness in this
article are based wholly on experimentally
determined log stability-constant values
determined in aqueous solutions at room
temperature. The values are not absolute;
addition of more metal ions might extend
the
scales
in
either
direction.
Small
differences between metal ions should not
be over-interpreted. The relative difference
scales are linear in log stability constant,
stretching from very hard at one end to very
soft at the other. As hardness decreases,
softness correspondingly increases, and
vice versa. These practical scales are not
comparable to that of Pearson, where
absolute hardness values are derived from
gas-phase parameters, and softness is the
reciprocal of hardness.
In practice, the principle of hard and
soft acids and bases is often contorted in
such a way as to provide nonfalsiFable
explanations for almost any observation.
The limitations of the principle need
greater exposure. The very hard Sc
3
+
and the very soft CH
3
Hg
+
both bind
strongly and nearly equally to the hard
ligands hydroxide on one hand and acetate
on the
other
(Table 1).
Though
both
metal ions are considered as very soft,
Hg
2
+
is among the strongest binders to
hydroxide and acetate, and Ag
+
among
the weakest. Many other such anomalies
may be found by considering differences
of stability-constant logs. It is only when
these differences are compared that one
Fnds some quantitative justiFcation for
the principle of hard and soft acids and
bases. The principle of hard and soft
acids and bases Fnds its most consistent
application not in direct stability-constant
comparisons but rather in the free energy
or log stability-constant differences of the
substitution reactions of Sect. 8.2.
9
Nonaqueous Environments
Nonaqueous solvents that lower the dielec-
tric constant increase stability constants
between oppositely charged ions, decrease
the constants between identically charged
ions, and leave relatively unaffected stabil-
ities with one neutral reactant species. ±or
example, on passing from water to a mixed
solvent system containing 70% by weight
dioxane, the dielectric constant drops from
79 to 18. This solvent change increases the
p
K
a
of acetic acid by 3.6 log units and de-
creases the p
K
a
of anilinium ion by 1.0
log unit. The much larger change in the
former case is due to the reaction between
oppositely charged proton and acetate be-
coming much more favored in the lower
dielectric medium. In contrast, the latter
reaction is merely transfer of a proton
from water to amine without the creation
or destruction of any charges.
Binding sites in proteins display lower
dielectric constants than the surrounding
water. An equivalent solution dielectric
constant applicable to binding sites in met-
alloproteins is calibrated with metal ion
stabilities in nonaqueous solvent mixtures.
±or the zinc ion active sites in bovine car-
bonic anhydrase and carboxypeptidase A,
the equivalent solution dielectric constants
are estimated as 35 and 70 respectively.
Theformerenzymereac
tsw
i
thasma
l
ler
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