# HSAB theory

HSAB concept is an initialism for "hard and soft (Lewis) 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 concept is a way of applying the notion of orbital overlap to specific chemical cases.[citation needed]

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. In 2005 it was shown that even the sensitivity and performance of explosive materials can be explained on basis of HSAB theory.[2]

Ralph Pearson introduced the HSAB principle in the early 1960s[3][4][5] as an attempt to unify inorganic and organic reaction chemistry.[6]

## Theory

Hard-soft trends for acids and bases
Acids
Bases

Essentially, the theory states 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.

Comparing tendencies of hard acids and bases vs. soft acids and bases
Property Hard acids and bases Soft acids and bases
oxidation state high low or zero
polarizability low high
electronegativity (bases) high low
HOMO energy of bases[7][8] low higher
LUMO energy of acids[7][8] high lower (but > soft-base HOMO)
affinity ionic bonding covalent bonding
Examples of hard and soft acids and bases
Acids Bases
hard soft hard soft
Hydronium H3O+ Mercury CH3Hg+, Hg2+, Hg22+ Hydroxide OH Hydride H
Alkali metals Li+,Na+,K+ Platinum Pt2+ Alkoxide RO Thiolate RS
Titanium Ti4+ Palladium Pd2+ Halogens F,Cl Halogens I
Chromium Cr3+,Cr6+ Silver Ag+ Ammonia NH3 Phosphine PR3
Boron trifluoride BF3 Borane BH3 Carboxylate CH3COO Thiocyanate SCN
Carbocation R3C+ P-chloranil Carbonate CO32− Carbon monoxide CO
Lanthanides Ln3+ Bulk metals M0 Hydrazine N2H4 Benzene C6H6
Thorium, uranium Th4+, U4+ Gold Au+

Borderline cases are also identified: borderline acids are trimethylborane, sulfur dioxide and ferrous Fe2+, cobalt Co2+ caesium Cs+ and lead Pb2+ cations. Borderline bases are: aniline, pyridine, nitrogen N2 and the azide, chloride, bromide, nitrate and sulfate 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:

## Chemical hardness

Chemical hardness in electron volt
Acids Bases
Hydrogen H+ Fluoride F 7
Aluminium 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[9]

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:[9]

${\displaystyle \eta ={\frac {1}{2}}\left({\frac {\partial ^{2}E}{\partial N^{2}}}\right)_{Z}}$.

The factor of one-half is arbitrary and often dropped as Pearson has noted.[10]

An operational definition for the chemical hardness is obtained by applying a three-point finite difference approximation to the second derivative:[11]

{\displaystyle {\begin{aligned}\eta &\approx {\frac {E(N+1)-2E(N)+E(N-1)}{2}}\\&={\frac {(E(N-1)-E(N))-(E(N)-E(N+1))}{2}}\\&={\frac {1}{2}}(I-A)\end{aligned}}}

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,

${\displaystyle \mu =\left({\frac {\partial E}{\partial N}}\right)_{Z}}$,

from which an operational definition for the chemical potential is obtained from a finite difference approximation to the first order derivative as

{\displaystyle {\begin{aligned}\mu &\approx {\frac {E(N+1)-E(N-1)}{2}}\\&={\frac {-(E(N-1)-E(N))-(E(N)-E(N+1))}{2}}\\&=-{\frac {1}{2}}(I+A)\end{aligned}}}

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

${\displaystyle 2\eta =\left({\frac {\partial \mu }{\partial N}}\right)_{Z}\approx -\left({\frac {\partial \chi }{\partial N}}\right)_{Z}}$,

and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum softness, 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 heat (enthalpy) of formation of the Lewis acid-base adduct in a non-coordinating solvent. The ECW model is quantitative model that describes and predicts the strength of Lewis acid base interactions, -ΔH . The model assigned E and C parameters to many Lewis acids and bases. Each acid is characterized by an EA and a CA. Each base is likewise characterized by its own EB and CB. The E and C parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form. The equation is

-ΔH = EAEB + CACB + W

The W term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric acid or base. The equation predicts reversal of acids and base strengths. The graphical presentations of the equation show that there is no single order of Lewis base strengths or Lewis acid strengths.[12] The ECW model accommodates the failure of single parameter descriptions of acid-base interactions.

A related method adopting the E and C formalism of Drago and co-workers quantitatively predicts the formation constants for complexes of many 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.[13]

Another quantitative system has been proposed, in which Lewis acid strength toward Lewis base fluoride is based on gas-phase affinity for fluoride.[14] Additional one-parameter base strength scales have been presented.[15] However, it has been shown that to define the order of Lewis base strength (or Lewis acid strength) at least two properties must be considered. [16] For Pearson's qualitative HSAB theory the two properties are hardness and strength while for Drago’s quantitative ECW model the two properties are electrostatic and covalent .

## Kornblum's rule

An application of HSAB theory is the so-called Kornblum's rule (after Nathan Kornblum) which states that in reactions with ambident nucleophiles (nucleophiles that can attack from two or more places), 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)[17] 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.

According to findings, electrophilic alkylations at free CN occur preferentially at carbon, regardless of whether the SN1 or SN2 mechanism is involved and whether hard or soft electrophiles are employed. Preferred N attack, as postulated for hard electrophiles by the HSAB principle, could not be observed with any alkylating agent. Isocyano compounds are only formed with highly reactive electrophiles that react without an activation barrier because the diffusion limit is approached. It is claimed that the knowledge of absolute rate constants and not of the hardness of the reaction partners is needed to predict the outcome of alkylations of the cyanide ion.[18]

Recently, analogous observations were made for the reactions of phenolate anions with carbocations. In contrast to the predictions made by Kornblum’s rule, changing from SN1 to SN2 mechanism favors oxygen- over carbon attack. [19]

### Criticism

In 2011, Herbert Mayr et al. from Ludwig Maximilian University of Munich (LMU) published a critical review in Angewandte Chemie.[20] Consecutive analysis of various types of ambident organic system reveals that an older approach based on thermodynamic/kinetic control describes reactivity of organic compounds perfectly, while the HSAB principle actually fails and should be abandoned in the rationalization of ambident reactivity of organic compounds.

## References

1. ^ Jolly, W. L. (1984). Modern Inorganic Chemistry. New York: McGraw-Hill. ISBN 978-0-07-032760-3.
2. ^ [1] E.-C. Koch, Acid-Base Interactions in Energetic Materials: I. The Hard and Soft Acids and Bases (HSAB) Principle-Insights to Reactivity and Sensitivity of Energetic Materials, Prop.,Expl.,Pyrotech. 30 2005, 5
3. ^ Pearson, Ralph G. (1963). "Hard and Soft Acids and Bases". J. Am. Chem. Soc. 85 (22): 3533–3539. doi:10.1021/ja00905a001.
4. ^ Pearson, Ralph G. (1968). "Hard and soft acids and bases, HSAB, part 1: Fundamental principles". J. Chem. Educ. 1968 (45): 581–586. Bibcode:1968JChEd..45..581P. doi:10.1021/ed045p581.
5. ^ Pearson, Ralph G. (1968). "Hard and soft acids and bases, HSAB, part II: Underlying theories". J. Chem. Educ. 1968 (45): 643–648. Bibcode:1968JChEd..45..643P. doi:10.1021/ed045p643.
6. ^ [2] R. G. Pearson, Chemical Hardness - Applications From Molecules to Solids, Wiley-VCH, Weinheim, 1997, 198 pp
7. ^ a b c IUPAC, Glossary of terms used in theoretical organic chemistry, accessed 16 Dec 2006.
8. ^ a b Miessler G.L. and Tarr D.A. "Inorganic Chemistry" 2nd ed. Prentice-Hall 1999, p.181-5
9. ^ a b Robert G. Parr & Ralph G. Pearson (1983). "Absolute hardness: companion parameter to absolute electronegativity". J. Am. Chem. Soc. 105 (26): 7512–7516. doi:10.1021/ja00364a005.
10. ^ Ralph G. Pearson (2005). "Chemical hardness and density functional theory" (PDF). J. Chem. Sci. 117 (5): 369–377. CiteSeerX 10.1.1.693.7436. doi:10.1007/BF02708340.
11. ^ Delchev, Ya. I.; A. I. Kuleff; J. Maruani; Tz. Mineva; F. Zahariev (2006). Jean-Pierre Julien; Jean Maruani; Didier Mayou (eds.). Strutinsky's shell-correction method in the extended Kohn-Sham scheme: application to the ionization potential, electron affinity, electronegativity and chemical hardness of atoms in Recent Advances in the Theory of Chemical and Physical Systems. New York: Springer-Verlag. pp. 159–177. ISBN 978-1-4020-4527-1.
12. ^ Vogel G. C.;Drago, R. S. (1996). "The ECW Model". Journal of Chemical Education. 73 (8): 701–707. Bibcode:1996JChEd..73..701V. doi:10.1021/ed073p701.CS1 maint: Uses authors parameter (link)
13. ^ Hancock, R. D.; Martell, A. E. (1989). "Ligand design for the selective complexation of metal ions in aqueous solution". Chemical Reviews. 89 (8): 1875–1914. doi:10.1021/cr00098a011.
14. ^ Christe, K.O.; Dixon, D.A.; McLemore, D.; Wilson, W.W.; Sheehy, J.A.; Boatz, J.A. (2000). "On a quantitative scale for Lewis acidity and recent progress in polynitrogen chemistry". Journal of Fluorine Chemistry. 101 (2): 151–153. doi:10.1016/S0022-1139(99)00151-7. ISSN 0022-1139.
15. ^ Laurence, C. and Gal, J-F. Lewis Basicity and Affinity Scales, Data and Measurement, (Wiley 2010) p 51 ISBN 978-0-470-74957-9
16. ^ Cramer, R. E., and Bopp, T. T. (1977) Great E and C plot. Graphical display of the enthalpies of adduct formation for Lewis acids and bases. Journal of Chemical Education 54 612-613
17. ^ The Mechanism of the Reaction of Silver Nitrite with Alkyl Halides. The Contrasting Reactions of Silver and Alkali Metal Salts with Alkyl Halides. The Alkylation of Ambident Anions Nathan Kornblum, Robert A. Smiley, Robert K. Blackwood, Don C. Iffland J. Am. Chem. Soc.; 1955; 77(23); 6269-6280. doi:10.1021/ja01628a064
18. ^ Tishkov, Alexander A.; Mayr, Herbert (2004). "Ambident Reactivity of the Cyanide Ion: A Failure of the HSAB Principle". Angewandte Chemie International Edition. 44 (1): 142–145. doi:10.1002/anie.200461640. PMID 15599920.
19. ^ Mayer, Robert J.; Breugst, Martin; Hampel, Nathalie; Ofial, Armin R.; Mayr, Herbert (2019-06-26). "Ambident Reactivity of Phenolate Anions Revisited: A Quantitative Approach to Phenolate Reactivities". Journal of Organic Chemistry. doi:10.1021/acs.joc.9b01485.
20. ^ Mayr, Herbert (2011). "Farewell to the HSAB Treatment of Ambident Reactivity". Angewandte Chemie International Edition. 50 (29): 6470–6505. doi:10.1002/anie.201007100. PMID 21726020.