HSAB theory

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Ralph Pearson lecturing in Northwestern University in 1969.

The HSAB concept, also known as HSAB theory, is widely used in chemistry for explaining stability of compounds, reaction paths etc. HSAB is the acronym for hard and soft acids and bases 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.

Ralph Pearson introduced the Hard Soft Acid Base (HSAB) principle in the early 1960s ^[2] ^[3] as an attempt to unify inorganic and organic reaction chemistry.

[edit] Theory

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.^[4] 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 size
high oxidation state
low polarizability
high electronegativity
energy low-lying HOMO (bases) or energy high-lying LUMO (acids).^[4]

Examples of hard acids are: H⁺, alkali ions, Ti⁴⁺, Cr³⁺, Cr⁶⁺, BF₃. Examples of hard bases are: OH^–, F^–, Cl^–, NH₃, CH₃COO^–, CO₃^2–.

Soft acids and bases tend to have large size, low or zero oxidation state, high polarizability, low electronegativity, energy high-lying HOMO (bases) and energy-low lying LUMO (acids).^[4] Examples of soft acids are: CH₃Hg⁺, Pt⁴⁺, Pd²⁺, Ag⁺, Hg²⁺, Hg₂²⁺, Cd²⁺, BH₃. Examples of soft bases are: H^–, R₃P, SCN^–, I^–

Acids				Bases
hard		soft		hard		soft
Hydrogen	H⁺	Mercury	CH₃Hg⁺, Hg²⁺, Hg₂²⁺	Hydroxyl	OH^-	Hydride	H^-
Alkali metals	Li⁺,Na⁺,K⁺	Platinum	Pt⁴⁺	Alcohol	RO^-	Thiol	RS^-
Titanium	Ti⁴⁺	Palladium	Pd²⁺	Halogens	F^-,Cl^-	Halogens	I^-
Chromium	Cr³⁺,Cr⁶⁺	Silver	Ag⁺	Ammonia	NH₃	Phosphine	PR₃
Boron trifluoride	BF₃	borane	BH₃	carboxylic acid	CH₃COO^-	Thiocyanate	SCN^-
Carbocation	R₃C⁺	P-chloranil		Carbonate	CO₃^2-	carbon monoxide	CO
		bulk Metals	M⁰	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 sulphate anions.

Generally speaking, acids and bases interact and the most stable interactions are hard-hard (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 dimethylsulfoxide 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.

[edit] Chemical hardness

Chemical hardness
Acids			Bases
Hydrogen	H⁺	infinite	Fluoride	F^-	7
Aluminum	Al³⁺	45.8	Ammonia	NH₃	6.8
Lithium	Li⁺	35.1	hydride	H^-	6.8
Scandium	Sc³⁺	24.6	carbon monoxide	CO	6.0
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
Iodine	I₂	3.4	Methane	CH₃^-	4.0
Table 2. Chemical hardness data

In 1983 Pearson together with Robert Parr extended the qualitative HSAB theory with quantitative chemical hardness (η) defined as ^[5]:

$\eta = 0.5(I - A) \,$

with $I\,$ the ionization potential and $A\,$ the electron affinity.

When the electronegativity (χ) as the Mulliken scale:

$\chi = 0.5(I + A) \,$

is the first derivative in a plot of energy $E\,$ versus the amount of electrons $N\,$ with fixed nuclear charge $Z\,$ in an atom or molecule:

$\chi = \left(\frac{\partial E}{\partial N}\right)_Z \,$

then the chemical hardness is simply the second derivative:

$\eta = 0.5\left(\frac{\partial^2 E}{\partial N^2}\right)_Z \,$

Hardness and electronegativity are related as:

$2\eta = -\left(\frac{\partial \chi}{\partial N}\right)_Z \,$

and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum softness.

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⁺.

[edit] References

^ Jolly, W. L.. Modern Inorganic Chemistry. ISBN 0070327602.
^ Pearson, Ralph G. (1963). "Hard and Soft Acids and Bases". J. Am. Chem. Soc. 85 (22): 3533 - 3539. DOI:10.1021/ja00905a001.
^ Pearson, Ralph G.. "Hard and soft acids and bases, HSAB" (subscriber access). J. Chem. Educ. 1968 (45): 581643.
^ ^a ^b ^c IUPAC, Glossary of terms used in theoretical organic chemistry, accessed 16 Dec 2006.
^ Absolute hardness: companion parameter to absolute electronegativityRobert G. Parr and Ralph G. Pearson J. Am. Chem. Soc.; 1983; 105(26) pp 7512 - 7516; DOI:10.1021/ja00364a005