Actually this article should be a part of the studies on coordination compounds, but is considered here because of the use of the term Hard and Soft Acids and Bases, and the ligands and metal ions are considered as Lewis bases and acids respectively (Article 1.3)

For some time, the coordination chemists have been aware that certain ligands tend to form their most stable complexes with heavier ions with nearly full d orbital electrons (Ag⁺, Hg²⁺, Pt²⁺) while others prefer metal ions with no d orbital electrons (Al³⁺, Ti⁴⁺). Based on this preferential bonding, metal ions have been classified as class (a) metals (alkali metal ions, alkaline earth metal ions, etc.) and class (b) metals (heavier metal ions or metal ions in low oxidation states, e.g., Ag⁺, Cu⁺,  Hg²⁺, Pt²⁺). Accordingly, ligands are classified as class (a) ligands and class (b) ligands depending on whether they form their stronger complexes with class (a) metal ions or class (b) metal ions respectively. Thus phosphines and thioethers form their strongest complexes with metal ions like Pd²⁺,  Hg²⁺, Pt²⁺ and are called class (b) ligands. On the other hand, ammonia, water or fluoride ions form their strongest complexes with ions like Be²⁺ and Ti⁴⁺ and are called class (a) ligands.

1.4.1.1 Order of Donor Atoms

For class (a) ligands, the order of stability constants of the metal complexes with a metal ion with different donor atoms is in the order:

N > P > As > Sb;    O > S . Se > Te; and  F > Cl > Br > I

For class (b) ligands, the order of the donor atoms is, however,

N < P < As < Sb;   O < S < Se, Te;  and F < Cl < Br < I.

1.4.1.2 Pearson’s Hard and Soft Acid and base (HSAB) Concept

In 1963, Pearson proposed the terms hard and soft can be used in place of the terms class (a) and class (b) respectively. Thus, a hard metal ion tends to coordinate most favorably with a hard ligand, whereas a soft metal ion tends to coordinate most favorably with a soft ligand. As the ligands are Lewis bases and the metal ions are Lewis acids, Pearson developed the term hard and soft acids and bases for this concept. Please note that Pearson’s rule is only an approximate qualitative indication of the relative stability of the metal complex, and is not a theory for explaining the observations.

1.4.2 ACID AND BASE STRENGTH OF HSAB

1.4.2.1 The Standard Reaction

The apparent preference for a hard and a soft ligand can be used to classify the metal ions as hard or soft, and vice versa for the ligands.

A base B can be classified as hard or soft depending on whether the equilibrium constant K for the following reaction is less than or more than unity:

BH⁺  + MeHg⁺⇌ MeHgB⁺ + H⁺

K = ([MeHgB⁺][H⁺]) / ([MeHg⁺][BH⁺]) 

= ([MeHgB⁺]) / ([MeHg⁺][B]) × ([H⁺][B]) / ([BH⁺])

= K₁K_a

or,    log K = log K₁ + log K_a

where K₁ can be taken as the formation constant of the complex MeHgB⁺, and K_a is the usual acid dissociation constant for the conjugate acid BH⁺. Therefore, hardness or softness is measured by the difference in the formation (stability) constant for the methylmercury(1+) – base  complex and the usual acid ionization constant for the conjugated acid. For hard base, the pK_a is more than the log ­K₁ value, whereas for the soft base, the pK_a is less than the log ­K₁ value.

Ordinarily, a hard base will drive the above reaction to the left, while a soft base will drive the reaction to the right. Methylmercury(1+) cation is selected as the standard base because (1) it is a typical soft acid and (2) a univalent cation that makes the calculations easier.

1.4.2.2 Classification of Metals Ions

Typical hard cations are the metal cations of group 1 to 4 in the highest oxidation states. and vanadium(V), chromium(VI), manganese(VII), iron(III) and cobalt(III). Boron trifluoride and trichloride and aluminium trichloride and methyltin(IV) are also hard acids.

Typical soft cations are metal cations of groups 11 and 12 in lower oxidation states (zero or 1). Bulk metals and non-metals are also soft acids. Gallium trichloride and tribromide are soft acids.

There are no hard and fast rules and many borderline cases also exist, e.g. divalent nearly full d orbitals of electrons like Cu²⁺, Ni²⁺, Co²⁺, Zn²⁺, Ru²⁺, Rh²⁺, Sb³⁺ and Bi^3.+. Non-metals in bulk (zero oxidation state) are soft, but become hard acids on higher oxidation states. Further, not all hard ions are equally hard: caesium ions are certainly softer than smaller lithium or sodium ions.

1.4.2.3 Classification of Ligands

Typical hard bass are amines, ammonia, water, hydroxide, fluoride, chloride

Soft bases are cyanide, thiosulphate, thioalkoxides, and iodide.

Aniline, pyridine and bromide are borderline bases. Though ammonia is typically hard, presence of easily polarizable aromatic rings as in aniline and pyridine and makes them borderline cases.

Hardness and softness refer to the hard–hard and soft–soft interactions and are different from the inherent  acid–base strengths.

Example 1: Both hydroxide and fluoride ions are hard bases, yet hydroxide ions (pK_a  = 15.7) are about 10¹³ times more basic than fluoride ions (pK_a= 2.85). A strong acid (or base) may replace a weaker acid, even when it appears to violate the HSAB principles. For example, sulphate ions,a stronger softer base can displace a weaker hard base fluoride from a hard acid hydronium ions (HF):

SO₄^2– + HF → HSO₄^– + F^–   (K_eq = 10⁴)

Similarly, a very strong hard base hydroxide can displace a softer base from a soft methylmercury(1+) cations:

OH^–  + CH₃HgSO₃^– → CH₃HgOH⁺ + SO₃^2–     (K_eq = 10).

In these examples, the strength of the bases (hard – hard interactions) are in the order

OH^– (15.7) > SO₃^2– (8.8) > F^– (2.85)

and force these reactions against the hard – soft principles. Nevertheless, if both the strengths and hardness are considered, the hard – soft rule works well:

HSO₃^–  + CH₃HgF→HF + CH₃HgSO₃^–    (K_eq = 10⁴)

HSO₃^–  + CH₃HgOH→2H₂O + CH₃HgSO₃^–   (K_eq = 10⁴)

Example 2: Both sulphide and hydroxyl ions combine with H⁺ ions (pK_a = 14.2 and 15.7 respectively). The K₁ for sulphide ions for methylmercury(II) cation is 21.2, but that for hydroxyl ions is only 9.4. Therefore, sulphide ion is considered as a soft base.

Example 3: Such anions also exist for which both K₁ as well as K_a are low or almost have the same order, (fluoride ions, pK_a=2.85, K₁ = 1.50) and sulphite ions, pK_a= 6.8 logK₁ = 8.1. In such cases, the slightly advantageous numerical value of the constant K₁ tilts the scales towards hard base (in keeping with smaller size and poor polarizability of the anion) for fluoride and towards softer base for sulphite ions.

The bonding between the hard acids and hard bases is predominantly ionic. Hard acids have no electrons in their valence shells and can accept electrons easily from the bases. Hard bases have completely filled outer valence shells and can donate their valence shell electron pairs through σ bonding. 

Soft – soft interactions give largely covalent compounds. The weak acid and base interaction the π bonding seems to be important.

1.4.3 BASIS FOR HARDNESS AND SOFTNESS

Typical hard acids and bases form ionic compounds. Since the electrostatic energy of an ion pair (Madelung energy) is inversely proportional to inter-ionic distance, the smaller is the ions, the more should be its stability. Since the electrostatic interactions cannot explain the soft – soft interactions because of a bigger size of the ions, it is assumed that these interactions are covalent in nature. In this context, polarization of d orbitals becomes important. Almost all soft metal ions gave six or more valence shell d orbital electrons; and a d¹⁰ configuration makes an excellent soft acids (Ag⁺, Hg²⁺).

Considering hard interactions as ionic and soft interactions as covalent, Misons and co-workers (1967) proposed the relation

pK = – log K = aX + by + c

In this equation,

K = equilibrium constant for the dissociation of the metal – ligand complex,
X, Y = parameters for metal ions,
a,b = parameters for the ligands,
c = a constant for the ligand to adjust the pK values so that all the values are on the same scale.

The parameters X and a can be considered as a measure of the hardness and include inherent acid – base strength also. X is closely related to electronegativity of the metal ion and measures its tendency to accept electrons from the ligands. It varies in the similar manner as the Irwin – Williams order for metal ions for the coordinate complexes:

Mn(II) < Fe(II) < Co(II) < Ni(II) < Cu(II) > Zn(II)

Inherent strength of the hardness – softness factor (a) tends to get mixed up as the Mison’s equation can be interpreted in two ways.

1. Pearson(1968) suggested that it is a measure of strength s as perturbed by a softness factor.
2. Drago and his co-workers (1972) suggested that hardness and softness factors can be built up together with the inherent strength into each factor and the parameter measure the strength of a hard species as a soft species.

The parameter Y indicates softness and can be evaluated from atomic parameters. Hard ions are observed to have Y less than 2.8, soft ions have Y more than 3.2;

[Hard acids]  Li⁺ (0.36) < Al³⁺ (0.70) < Mg²⁺ (0.87)
< Na⁺ (0.93) < K⁺ (0.93) <Ca²⁺ (1.62) < Fe³⁺ (2.37)
< Co²⁺ (2.56) < Cs⁺ (2.73) < Co²⁺ (2.96) < Sn²⁺ (3.17)
< Tl³⁺ (3.2) < Cu⁺ (3.45) < Pb²⁺ (3.58) < Tl⁺ (3.78)
< Hg²⁺ (4.25) < Au⁺ (5.95)   [Soft Acid]

The parameter b increases with the softness of the ligand:

OH^– (0.40) < NH₃ (1.08) < Cl^– (2.49) < Br^– (5.58)
< I^– (7.17) < S₂O₃^2– (12.4)

The Pi (π) bonding Contribution: Chatt and Millikan suggested that the soft species have nearly full valence shell d orbital electrons, and are easily polarisable, so that the pi(π) bonding contribution in the soft – soft interactions cannot be overlooked. Soft metal ions are generally metals in low oxidation states which have a high tendency to form covalent bonds. Good pi (π) binding ligands are all soft bases, Examples: phosphines, thioalkoxides or thiolates, carbon monoxide or iodide ions.

London’s Dispersion forces: These weak forces also cannot be ignored. They increase with the size and polarizability of the species and may stabilize the bonds between the large sized soft and easily polarizable species.

1.4.4 ELECTRONEGATIVITY AND HSAB CONCEPT

Generally, species with high electronegativity are hard and those with low electronegativity are soft. However, there is a difference between the Pauling’s electronegativity and Pearson’s concept. According to the Pauling‘s concept, the resonance energy leading to the stability of covalent hetero nuclear bond is proportional to the electronegativity of the bonded  atoms. Taken literally, it would imply that the highest stability will be the one having the atoms having the largest difference in their electronegativity. This would mean that the most stable bond will be that in CsF. Yet, reaction between CsF and LiI is exothermic.

CsF + LiI → LiF + CsI        (ΔH =  – 138 kJ mol^–1)

In this case, the soft – soft  interactions work better than the electronegativity differences. The apparent discrepancy can be explained by two possibilities.

1. Enthalpy of atomization of the four species are LiF = 573, CsF = 501, LiI = 347 and CsI = 335 (all values in kJ mol^–1). Though the hard – hard interactions are the strongest (573 kJ mol^–1), and soft – soft interactions are the weakest (335 kJ mol^–1), it seems that the driving force of the reaction is the hard – hard interactions. One can consider the soft – soft interactions, and still arrive at the same conclusion.

On can consider another reaction:

HgF₂    +    BeI₂    →    BeF₂   +    HgI₂
soft-hard  hard-soft             hard-hard  soft-soft
535          577                1262        292 (kJ mol^–1)

The enthalpy of atomization shows that in this case also, the hard – hard interactions (1262 kJ mol^–1) are the strongest and drive the reaction forward. The calculated enthalpy of reaction (1262 + 292) – (535 +577) = 1554 – 1112 = 432 kJ mol^–1) compares well with the observed enthalpy of reaction (397 kJ mol^–1).

2. The bonding energies of a molecule can be divided into ionic, covalent bond energies, etc. Considering the bonds to be completely covalent (assuming that the atoms have zero partial charge on them), the bond energy with bee inversely proportional to the internuclear bond distance. Smaller atoms will form stronger bonds. Exceptions are N–N, O–O and F–F bonds due to non-bonded inter-electronic repulsions. Hence, the hard – hard interaction cannot be considered purely electrostatic in nature. There must be some covalent contribution also. Calculations show that for LiF, nearly one-fourth of its bond energy (573 kJ mol^–1) comes from its covalent bond energy, one-half is the Madelung electrostatic energy due to partial ionic charges (about 2/3 electronic charge) on the bonded atoms, and one-fourth from the transfer of charge from more electropositive lithium atom to more electronegative fluorine atom (corresponding to the Pauling’s ionic resonance energy).

1.4.5 APPLICATIONS OF HSAB CONCEPT

Though a quantitative data for hardness and softness is bot presently available, it helps in correlating a number of diverse observed reactions. Some examples are given below.

1. It explains the stability of [AgI₂]^– due to strong soft – soft interactions. At the same time, instability of [AgF₂]^– is unstable as it involves soft – hard interactions.
2. Reaction between LiI (hard cation + soft anion) and CsF (soft cation + hard anion) proceeds to form products that contain the soft cation (silver)H with soft anion (iodide) and a hard cation (lithium) with a hard anion (fluoride):

LiI + CsF → LiF + CsI       (ΔH =  – 138 kJ mol^–1)

3. Pearson has stated that soft metals adsorb soft bases and thereby, explains catalytic reactions.
4. Jφrgenson suggested that the hard and soft ligands tend to group together separately. 
5. Hard solvents are expected to dissolve hard solutes. In both the nucleophilic and electrophilic substitution reactions, the reaction rates can be correlated with the hard – soft nature of the acidic and basic centres.
6. Jφrgenson (1968) has referred to the tendency of soft ligands to combine with a centre already having soft ligands, and vice versa , as symbiosis. He has explained that such compounds are substituted symmetrically and do not have a mixed substitution.

BHF₃^– + BH₃F^– → BH₄^– + BF₄^–
CH₃F + CHF₃→ CH₄ + CF₄
BF₃ + F^–→ BF₄^–
B₂H₆ + 2H^–→ 2BH₄^–

The hardness and softness of a compound is not an inherent property, but depends upon the substitutents. Thus, ammonia is a hard base, but pyridine is a borderline case. Electron withdrawing and small sized nonpolarizable substituents like fluoride, make the compound a harder species. On the other hand, electron-releasing and polarizable substituents make the species softer.

1.4.6  LIMITATIONS OF HSAB CONCEPT

1. The chief limitation of the HSAB concept is its general nature without any quantitative scale of measurement.
2. The arbitrariness permitted to break a compound into acid and base fragments in order to explain the reaction is convenience only when the reaction is known. For example, the break I for the esterification reaction explains the observed reaction, there is nothing to exclude break II on the basis of hard – soft interactions:

Break I  : CH₃CO⁺OH^– + C₂H₅^–OH⁺
Break II : CH₃COO^–H⁺ + C₂H₅⁺OH^–

3.  As the hard – soft factors are independent ofacidic or basic character of the compound, they work independently. Many examples have already been considered to show the inter-dependence of the two concepts.

 4.   Consider a reaction

CH₃(g)⁺ + H₂(g)  → CH₄(g) + H(g)⁺

which should proceed due to soft – soft interactions. However, unfavourable entropy change (+397 kJ mol^–1) of the reaction does not permit the reaction to proceed at all. This may also be due to the greater acidity of hydronium ions as compared to the CH₃(g)⁺ cations.

It can be summarized that the HSAB concept is useful in for the following.

1. It systematizes a large number of observations regarding the relative stability of the coordination compounds.
2. In general, the soft – soft interactions are not the driving force of the reactions. They are merely the consequences of the hard – hard interactions forming the compounds.
3. For metal ions which can expand their valence shell octet, the soft – soft interactions may become the driving force. But, this is presently only a conjecture.