When we consider general acids such as Al3+, Cr3+,
and BF3, we find there are good correlations between
the order of affinity to bases obtained with them and the order
obtained when H+ is used as the acid. However, a different
order is observed for an acid such as Hg2+.
We need to consider two main classes of substance, the hard
and soft acids and bases. This is
a distinction between two types of behaviour, class
a and class b, which depends
on the order of the strengths (measured in terms of the equilibrium
constant for formation of the complex) with which the substance
forms complexes with halide ion bases.
Class A substances form bonds to the halide ions in the order:
Class B substances form bonds to the halide ions in the order:
Hard acids are those substances which belong to class A, and
soft acids are those which belong to class B.
For Al3+, a strong acid, the binding strength increases
with the charge to size ratio of the anion, which is consistent
with an electrostatic picture of the bonding. For Hg2+,
a weak acid, the binding strength increases with the polarizability
of the anion. These observations suggest that hard acid cations
form complexes in which simple coulombic interactions are dominant,
and soft acid cations form complexes in which covalent bonding
Similarly, the Lewis acid phenol forms a more stable complex
with (C2H5)2O than (C2H5)2S,
and so is a hard acid, whereas I2 forms a more stable
complex with (C2H5)2S, and so
is a soft acid.
A general description is shown below:
If follows from the definition of hard and soft
acids that bases can similarly be classified:
Hard acids tend to
bind to hard bases, and soft acids tend to bind to soft bases.
The bonding between hard acids and bases can be
described in terms of ionic or dipole-dipole interactions, whereas
soft acids and bases are more polarizable, and the bonding is
Hardness and softness can be interpreted
in terms of the separations of the frontier molecular orbitals,
ie. the HOMO-LUMO gap. When the gap is small, the
electron distribution is easily distorted, and so the polarizability
is high and the molecule is soft.
When the gap is large, the ability to distort is small,
even in a strong field, and the molecule is hard, as it
is unable to distort its electrons. Interactions between
these species are thus primarily electrostatic.
A hard acid does not have a low lying LUMO, and a hard
base has a low energy, or strongly bound, HOMO.
The absolute hardness of a species
can be defined as half the HOMO-LUMO gap, ie. ηM
in the diagram. This can be related to the ionization enthalpy
and the electron affinity:
In the above diagram, it should be noted that both species have
the same electronegativity, χM,
but have very different behaviour as acids and bases.
The concepts of hardness and softness help to
rationalize much of inorganic chemistry., but must be used with
regard to other factors which influence the outcome of reactions.
The Goldschmidt classification of
the elements is much used in geochemistry, and can partly be explained
by the tendency of hard acids to bind with hard bases, and of
soft acids to bind with soft bases. In this scheme, two of the
classes of elements are lithophile elements
(those found in the earth's crust in silicate materials bound
to the hard base O2-) and chalcophile
elements (those found in combination with the soft bases
S2-, Se2- and Te2-).
The lithophiles are hard acids, and the chalcophiles are soft