HSAB theory
The HSAB concept is an acronym for 'hard and soft acids and bases'. Also known as the
Pearson acid base concept, HSAB is widely used in chemistry for explaining stability of
compounds, reaction mechanisms and pathways. It assigns the terms 'hard' or 'soft', and
'acid' or 'base' to chemical species. 'Hard' applies to species which are small, have high
charge states (the charge criterion applies mainly to acids, to a lesser extent to bases), and
are weakly polarizable. 'Soft' applies to species which are big, have low charge states and
are strongly polarizable.[1]
The theory is used in contexts where a qualitative, rather than quantitative description
would help in understanding the predominant factors which drive chemical properties and
reactions. This is especially so in transition metal chemistry, where numerous
experiments have been done to determine the relative ordering of ligands and transition
metal ions in terms of their hardness and softness.
HSAB theory is also useful in predicting the products of metathesis reactions. Quite
recently it has been shown that even the sensitivity and performance of explosive
materials can be explained on basis of HSAB theory.[2]
The gist of this theory is that soft acids react faster and form stronger bonds with soft
bases, whereas hard acids react faster and form stronger bonds with hard bases, all other
factors being equal.[7] The classification in the original work was mostly based on
equilibrium constants for reaction of two Lewis bases competing for a Lewis acid.
Hard acids and hard bases tend to have:





small atomic/ionic radius
high oxidation state
low polarizability
high electronegativity
energy low-lying HOMO (bases) or energy high-lying LUMO (acids).[7]
Examples of hard acids are: H+, alkali ions, Ti4+, Cr3+, Cr6+, BF3. Examples of hard bases
are: OH–, F–, Cl–, NH3, CH3COO–, CO32–. The affinity of hard acids and hard bases for
each other is mainly ionic in nature.
Soft acids and soft bases tend to have:





large atomic/ionic radius
low or zero oxidation state
high polarizability
low electronegativity
energy high-lying HOMO (bases) and energy-low lying LUMO (acids).[7]
Examples of soft acids are: CH3Hg+, Pt2+, Pd2+, Ag+, Au+, Hg2+, Hg22+, Cd2+, BH3.
Examples of soft bases are: H–, R3P, SCN–, I–. The affinity of soft acids and bases for
each other is mainly covalent in nature.
Acids
hard
Bases
soft
hard
soft
+
Hydronium H+
Mercury
CH3Hg ,
Hg2+,
Hydroxyl
Hg22+
OH-
Hydride
H-
Alkali
metals
Li+,Na+,K+ Platinum Pt2+
Alkoxide
RO-
Thiolate
RS-
Titanium
Ti4+
Palladium Pd2+
Halogens
F-,Cl-
Halogens
I-
NH3
Phosphine
PR3
Chromium Cr3+,Cr6+
Silver
Ag+
Ammonia
Boron
trifluoride
borane
BH3
Carboxylate CH3COO- Thiocyanate SCN-
BF3
Carbocation R3C+
Pchloranil
bulk
Metals
M0
Gold
Au+
Carbonate
CO32-
carbon
monoxide
CO
Hydrazine
N2H4
Benzene
C6H6
Table 1. Hard and soft acids and bases
Borderline cases are also identified: borderline acids are trimethylborane, sulfur dioxide
and ferrous Fe2+, cobalt Co2+ and lead Pb2+ cations. Borderline bases are: aniline,
pyridine, nitrogen N2 and the azide, bromine, nitrate and sulfate anions.
Generally speaking, acids and bases interact and the most stable interactions are hardhard (ionogenic character) and soft-soft (covalent character).
An attempt to quantify the 'softness' of a base consists in determining the equilibrium
constant for the following equilibrium:
BH + CH3Hg+ ↔ H+ + CH3HgB
Where CH3Hg+ (methylmercury ion) is a very soft acid and H+ (proton) is a hard acid,
which compete for B (the base to be classified).
Some examples illustrating the effectiveness of the theory:

Bulk metals are soft acids and are poisoned by soft bases such as phosphines and
sulfides.


Hard solvents such as hydrogen fluoride, water and the protic solvents tend to
solvatate strong solute bases such as the fluorine anion and the oxygen anions. On
the other hand dipolar aprotic solvents such as dimethyl sulfoxide and acetone are
soft solvents with a preference for solvatating large anions and soft bases.
In coordination chemistry soft-soft and hard-hard interactions exist between
ligands and metal centers.
Chemical hardness
In 1983 Pearson together with
Robert Parr extended the
qualitative HSAB theory with
a quantitative definition of the
chemical hardness (η) as
being proportional to the
second derivative of the total
energy of a chemical system
with respect to changes in the
number of electrons at a fixed
nuclear environment:[8]
Chemical hardness in electron volt
Acids
Bases
+
H
Aluminum
Al3+ 45.8
Ammonia
NH3 6.8
Lithium
Li+ 35.1
hydride
H-
Scandium
Sc3+ 24.6
carbon monoxide CO
Sodium
Na+ 21.1
hydroxyl
OH- 5.6
Lanthanum
La3+ 15.4
cyanide
CN- 5.3
Zinc
Zn2+ 10.8
phosphane
PH3 5.0
Carbon dioxide CO2 10.8
nitrite
NO2- 4.5
Sulfur dioxide SO2 5.6
Hydrosulfide
SH- 4.1
Methane
CH3- 4.0
Iodine
The factor of one-half is
arbitrary and often dropped as
Pearson has noted.[9]
I2
infinite Fluoride
F-
Hydrogen
3.4
7
6.8
6.0
Table 2. Chemical hardness data [8]
An operational definition for the chemical hardness is obtained by applying a three-point
finite difference approximation to the second derivative:[10]
where I is the ionization potential and A the electron affinity. This expression implies that
the chemical hardness is proportional to the band gap of a chemical system, when a gap
exists.
The first derivative of the energy with respect to the number of electrons is equal to the
chemical potential, μ, of the system,
from which an operational definition for the chemical potential is obtained from a finite
difference approximation to the first order derivative as
which is equal to the negative of the electronegativity (χ) definition on the Mulliken
scale: μ = −χ.
The hardness and Mulliken electronegativity are related as
and in this sense hardness is a measure for resistance to deformation or change. Likewise
a value of zero denotes maximum softness, where softness is defined as the reciprocal of
hardness.
In a compilation of hardness values only that of the hydride anion deviates. Another
discrepancy noted in the original 1983 article are the apparent higher hardness of Tl3+
compared to Tl+.
Modifications
If the interaction between acid and base in solution results in an equilibrium mixture the
strength of the interaction can be quantified in terms of an equilibrium constant. An
alternative quantitative measure is the standard heat (enthalpy) of formation of the adduct
in a non-coordinating solvent. Drago and Wayland proposed a two-parameter equation
which predicts the formation of a very large number of adducts quite accurately.
–ΔHO (A—B) = EAEB + CACB
Value of the E and C parameters can be found in Drago et al.[11] Hancock and Martell
found that an E and C equation analogous to that of Drago gave an excellent quantitative
prediction of formation constants for complexes of 34 metal ions plus the proton with a
wide range of unidentate Lewis acids in aqueous solution, and also offered insights into
factors governing HSAB behavior in solution [12]
Another quantitative system as been proposed, in which Lewis acid strength is based on
gas-phase affinity for fluoride. [13]
Kornblum's rule
An application of HSAB theory is the so-called Kornblum's rule which states that in
reactions with ambident nucleophiles, the more electronegative atom reacts when the
reaction mechanism is SN1 and the less electronegative one in a SN2 reaction. This rule
(established in 1954) [14] actually predates HSAB theory but in HSAB terms its
explanation is that in a SN1 reaction the carbocation (a hard acid) reacts with a hard base
(high electronegativity) and that in a SN2 reaction tetravalent carbon (a soft acid) reacts
with soft bases.
Hard and Soft Acids and Bases.
We have already pointed out that the affinity that metal ions have for ligands is controlled by
size, charge and electronegativity. This can be refined further by noting that for some metal
ions, their chemistry is dominated by size and charge, while for others it is dominated by their
elctronegativity. These two categories of metal ions have been termed by Pearson as hard metal
ions and soft metal ions. Their distribution in the periodic table is as follows:
Figure 1. Table showing distribution of hard, soft, and intermediate Lewis Acids in the Periodic
Table, largely after Pearson.
Pearson’s Principle of Hard and Soft Acids and Bases (HSAB) can be stated as follows:
Hard Acids prefer to bond with Hard Bases, and Soft Acids prefer to bond with Soft Bases. This
can be illustrated by the formation constants (log K1) for a hard metal ion, a soft metal ion, and
an intermediate metal ion, with the halide ions in Table 1:
Table 1. Formation constants with halide ions for a representative hard, soft, and intermediate
metal ion .
________________________________________________________________________
Log K1
F-
Cl-
Br-
I-
classification
________________________________________________________________________
Ag+
0.4
3.3
4.7
6.6
Pb2+
1.3
0.9
1.1
1.3
Fe3+
6.0
1.4
0.5
-
soft
intermediate
hard
________________________________________________________________________
What one sees in Table 1 is that the soft Ag+ ion strongly prefers the heavier halide ions Cl-, Br-,
and I- to the F- ion, while the hard Fe3+ ion prefers the lighter F- ion to the heavier halide ions.
The intermediate Pb2+ ion shows no strong preferences either way. The distribution of
hardness/softness of ligand donor atoms in the periodic Table is as follows:
Figure 2. Distribution of hardness and softness for potential donor atoms for ligands in the
Periodic Table. The diagram shows that hardness increases toward F-, and softness increases
away from F-. However, this is not a smooth transition. There is, as shown, a major discontinuity
between the lighter members of each group, namely, F-, O, and N, and their heavier congeners.
Thus, Cl-, Br-, and I- are far more like each other, and far different from F-, in their bonding
preferences, as can be seen in Table 1.
The hardness of ligands tends to show, as seen in Figure 2, a discontinuity between the lightest
member of each group, and the heavier members. Thus, one finds that the metal ion affinities of
NH3 are very different from metal ion affinities for phosphines such as PPh3 (Ph = phenyl), but
that the complexes of PPh3 are very similar to those of AsPh3. A selection of ligands classified
according to HSAB ideas are:
HARD:
SOFT:
H2O, OH-, CH3COO-, F-, NH3, oxalate ( -OOC-COO-), en.
Br-, I-, SH-, (CH3)2S, S=C(NH2)2 (thiourea), P(CH3)3, PPh3, As(CH3)3, CNS-C≡N (thiocyanate S-bound)
INTERMEDIATE: C6H5N (pyridine), N3- (azide), -N=C=S (thiocyanate, N-bound), Cl-
The softest metal ion is the Au+(aq) ion. It is so soft that the compounds AuF and Au2O are
unknown. It forms stable compounds with soft ligands such as PPh3 and CN-. The affinity for CN-
is so high that it is recovered in mining operations by grinding up the ore and then suspending it
in a dilute solution of CN-, which dissolves the Au on bubbling air through the solution:
4 Au(s) + 8 CN-(aq) + O2(g) + 2 H2O = 4 [Au(CN)2]-(aq) + 4 OH- [1]
The aurocyanide ion is linear, with two-coordinate Au(I). This is typical for Au(I), that it prefers
linear two-coordination. This coordination geometry is seen in other complexes of Au(I), such as
[AuPPh3Cl], for example. Neighboring metal ions such as Ag(I) and Hg(II) are also very soft, and
show the unusual preference for two-coordination.
An example of a very hard metal ion is Al(III). It has a high log K1 with F- of 7.0, and a reasonably
high log K1(OH-) of 9.0. It has virtually no affinity in solution for heavier halides such as Cl-. Its
solution chemistry is dominated by its affinity for F- and for ligands with negative O-donors.
One can rationalize HSAB in terms of the idea that soft-soft interactions are more covalent,
while hard-hard interactions are ionic. The covalence of the soft metal ions relates to their
higher electronegativity, which in turns depends on relativistic effects.
What one needs to be able to comment on is sets of formation constants such as the following:
Metal ion:
Ag+
Ga3+
Pb2+
Log K1(OH-):
2.0
11.3
6.0
Log K1(SH-):
11.0
8.0
6.0
What is obvious here is that the soft Ag+ ion prefers the soft SH- ligand to the hard OH- ligand,
whereas for the hard Ga3+ ion the opposite is true. The intermediate Pb2+ ion has no strong
preference. Another set of examples is given by:
Metal ion:
Ag+
H+
Log K1(NH3):
3.3
9.2
Log K1 (PPh3):
8.2
0.6
Again, the soft Ag+ ion prefers the soft phosphine ligand, while the hard H+ prefers the hard Ndonor.
Thiocyanate (SCN-) is a particularly interesting ligand. It can bind to metal ions either through
the S or the N. Obviously, it prefers to bind to soft metal ions through the S, and to hard metal
ions through the N. This can be seen in the structures of [Au(SCN)2]- and [Fe(NCS)6]3- in Figure 3
below:
Figure 3. Thiocyanate complexes showing a) N-bonding in the [Fe(NCS)6]3- complex with the hard
Fe(III) ion, and b) S-bonding in the [Au(SCN)2]- complex (CSD: AREKOX) with the soft Au(I) ion.
In general, intermediate metal ions also tend to bond to thiocyanate through its N-donors. A
point of particular interest is that Cu(II) is intermediate, but Cu(I) is soft. Thus, as seen in Figure
4, [Cu(NCS)4]2- with the intermediate Cu(II) has N-bonded thiocyanates, but in [Cu(SCN)3]2-, with
the soft Cu(I), S-bonded thiocyanates are present.
Figure 4. Thiocyanate complexes of the intermediate Cu(II) ion and soft Cu(I) ion. Note that at a)
the thiocyanates are N-bonded in [Cu(NCS)4]2- with the intermediate Cu(II), but at b) the
thiocyanates in [Cu(SCN)3]2-, with the soft Cu(I), are S-bonded (CSD: PIVZOJ).