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: I<Br<Cl<F

Class B substances form bonds to the halide ions in the order: F<Cl<Br<I

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 coulombicinteractions are dominant, and soft acid cations form complexes in which covalent bonding is important.

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:

Hard Acids Kf:
Soft Acids Kf:

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 more covalent.

Hardness and softness can be interpreted in terms of the separations of the frontier molecular orbitals, ie. the HOMOLUMO 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 acids.