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Pearson's Hard Soft [Lewis] Acid Base Principle
The HSAB Principle

Ralph Pearson introduced his Hard Soft [Lewis] Acid Base (HSAB) principle in the early nineteen sixties, and in doing so attempted to unify inorganic and organic reaction chemistry. The impact of the new idea was immediate, however, over the years the HSAB principle has rather fallen by the wayside while other approaches developed at the same time, such as frontier molecular orbital (FMO) theory and molecular mechanics, have flourished.

This page discusses the profound limitations of the Pearson approach and compares & contrasts the HSAB principle to the chemogenesis analysis as presented in this web book.

Note, in this web book:

Lewis acids are RED Lewis bases are BLUE

Irving-Williams Stability Series

The Irving-Williams stability series (1953) pointed out that for a given ligand the stability of dipositive metal ion complexes increase:

Ba2+  <  Sr2+  <  Ca2+  <  Mg2+  <  Mn2+  <  Fe2+  <  Co2+  <  Ni2+  <  Cu2+  <  Zn2+

It was also known that certain ligands formed their most stable complexes with metal ions like Al3+, Ti4+ & Co3+ while others formed stable complexes with Ag+, Hg2+ & Pt2+

Ahrland's Type A, Type B Analysis

In 1958 Ahrland et al. classified metal cations as Type A and Type B, where:

Type A metal cations include:

Type B metal cations include:

Ligands, chemical entities that complex with metal cations, were classified as Type A or Type B depending upon whether they formed more stable complexes with Type A metal cations or Type B metal cations, from here:

Ligand's tendency to complex
with Type A Metals
Ligand's tendency to complex
with Type B Metals

N  >>  P  >  As  >  Sb  >  Bi

O  >>  S  >  Se  >  Te

F  >>  Cl  >  Br  >  I

N  <<  P  >  As  >  Sb  >  Bi

O  <<  S  ~  Se  ~  Te

F  <  Cl  <  Br  <<  I

From this analysis, an empirical rule can be derived:

Type A Metals prefer to bind (complex) to Type A Ligands


Type B Metals prefer to bind (complex) to Type B Ligands

These empirical – experimentally derived – rules tell us that Type A Metals are more likely to form oxides, carbonates, nitrides and fluorides, while Type B Metals are more likely to form phosphides, sulfides and selinides.

Railsback's Geochemical Analysis

The "Type A, Type B" analysis is of great economic importance because:

This approach has been very successful developed in by Bruce Railsback with his excellent and highly recommended "Earth Scientist's Periodic Table website".

Click image to enlarge:

Pearson's HSAB Principle (The Hard Soft [Lewis] Acid Base Principle)

In the nineteen sixties, Ralph Pearson greatly expanded the Type A–Type B logic by explaining the differential complexation behaviour of cations and ligands in terms of electron pair accepting Lewis acids and electron pair donating Lewis bases:

Lewis acid  +  Lewis base   →   Lewis acid/base complex

Pearson classified Lewis acids and Lewis bases as hard, borderline or soft.

According to Pearson's hard soft [Lewis] acid base (HSAB) principle:

Hard [Lewis] acids prefer to bind to [complex with] Hard [Lewis] bases


Soft [Lewis] acids prefer to bind to [complex with] Soft [Lewis] bases

At first sight, the HSAB analysis seems rather similar to the Type A and Type B system.

However, Pearson classified a very wide range of atoms, ions, molecules and molecular ions as hard, borderline or soft, moving the analysis from traditional metal/ligand inorganic chemistry into – and combining with – the realm of organic chemistry.

Pearson's HSAB Classification System, from here:

Pearson's Hard Lewis Acids (from the Chemical Thesaurus), here, and from the congeneric array database, here:

Pearson's Borderline Lewis Acids, here, and here:

Pearson's Soft Lewis Acids, here, and here:

Pearson's Hard Lewis Bases (from The Chemical Thesaurus), here, and from the congeneric array database, here:

Pearson's Borderline Lewis Bases, here, and here:

Pearson's Soft Lewis Bases, here, and here:

Jensen's Review of the HSAB Principle

William (Bill) Jensen presented three papers in the ACS journal Chemistry, vol 47 (1974), Lewis Acid-Base Theory: Part I March pp 11-14; Part II April pp 13-18; Part III May pp 14-18. Part III deals with Pearson's HSAB analysis.

The combined paper – which is both excellent and detailed – is available on Bill's web space (and a clone of the file can be downloaded from this website).

Klopman's FMO Analysis

In 1968, G. Klopman attempted to quantify Pearson's HSAB principle using frontier molecular orbital (FMO) theory, as discussed elsewhere in this web book, here, with this equation:

Klopman proposed that:

Hard [Lewis] Acids bind [complex] to hard [Lewis] bases to give charge-controlled (ionic) complexes. Such interactions are dominated by the +/– charges on the interacting species.


Soft [Lewis] Acids bind [complex] to soft [Lewis] bases to give FMO-controlled [covalent] complexes. These interactions are dominated by the energies of the participating frontier molecular orbitals (FMO), the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

Read more elsewhere in the Chemogenesis web book, here, or look at Ian Fleming's Organic Chemistry and FMO theory here, where these ideas are developed at some length.

Using the above analysis, the contributing aspects of charge-controlled and FMO-controlled Lewis acid/base complexation are separated and quantified, a crucial development.

Combining Pearson's and Klopman's Ideas

Hard Lewis acids:
• Atomic centres of small ionic radius
• High positive charge
• Species do not contain electron pairs in their valence shells
• Low electron affinity
• Likely to be strongly solvated
• High energy LUMO

Soft Lewis acids:
• Large radius
• Low or partial δ+ positive charge
• Electron pairs in their valence shells
• Easy to polarise and oxidise
• Low energy LUMOs, but large magnitude LUMO coefficients

Hard Lewis bases:
• Small, highly solvated, electronegative atomic centres: 3.0–4.0
• Species are weakly polarisable
• Difficult to oxidise
• High energy HOMO

Soft Lewis bases:
• Large atoms of intermediate electronegativity: 2.5–3.0
• Easy to polarise and oxidise
• Low energy HOMOs but large magnitude HOMO coefficients

Borderline species have intermediate properties.

There is a qualifier in Klopman's paper saying that: it is not necessary for species to possess all properties.

The Ho Paper

Pearson suggested that hard-to-soft trends could be found amongst groups 15, 16 and 17 of the periodic table. In 1975 the idea was extended by Tse Lok Ho who used realistic chemical species and coined the term congeneric (of the same family), where congeneric species are isoelectronc (have the same outer shell Lewis structure).

[Your author has spent many, many hours reading this most interesting paper.]


Pearson, R.G., Hard and Soft Acids and Bases, JACS 85, 3533-3539 (1963)

  Ho, T.-L., The Hard Soft Acids Bases (HSAB) Principle and Organic Chemistry Chemistry Reviews 75, 1-20 (1975)

The HSAB Principle for Organic & Main Group Chemists

For our purposes – main group and organic reaction chemistry – the Pearson approach is most successful when comparing pairs of species:

This type of analysis can be very useful in explaining reaction selectivity.

For example, β-propiolactone – a reactive cyclic ester – is ring opened by nucleophilic Lewis bases. The attack can occur at two positions and nucleophiles exhibit regioselectivity:

There are quite a number of examples of ambidentate selectivity in The Chemical Thesaurus reaction chemistry database:

Problems, problems, problems...

However, there are severe problems with Pearson's analysis. While the Pearson-Klopman HSAB model is not exactly wrong... it does grossly simplify [over simplify] the known reaction chemistry, as recognised by Ralph Pearson himself:

At the beginning of his 1997 book, Chemical Hardness, Wiley-VCH, pp 3-4, Ralph Pearson candidly writes:

"With [the 'Hard-Soft'] nomenclature it is possible to make a simple, general statement:

"Hard acids prefer to coordinate to hard bases, and soft acids prefer to coordinate soft bases."

"This is the Principle of Hard and Soft Acids and Bases, or the HSAB Principle.

"Note that this Principle is simply a restatement of the experimental evidence which led to [the classification system in the first place]. It is a condensed statement of a very large amount of chemical information. As such it might be called a law. But this label seems pretentious in view of the lack of a quantitative definition of hardness.

"HSAB is not a theory, since it does not explain variations in the strength of chemical bonds. The word 'prefer' in the HSAB Principle implies a rather modest effect.

"Softness is not the only factor which determines the value of ΔH° in the equation:

A      +      :B       →       A:B

"There are many examples of very strong bonds between mismatched pairs, such as H2, formed from hard H+ and soft H.

"H2O, OH and O2– are all classified as hard bases, but there are great differences in their base strength, by any criterion."


Indeed so...     (!)

One problem is that the full set of hard-borderline-soft interactions and complexations is simply not considered using the Pearson analysis. Look how empty the HSAB interaction matrix is:

The Pearson HSAB principle states that "hard [Lewis] acids prefer to bind to hard [Lewis] bases and that soft [Lewis] acids prefer to bind to soft [Lewis] bases", which may be true, but it says nothing about mixed hard-soft complexes.

Klopman simply states – very unhelpfully – that such interactions are "undefined"!

Yet, many of the most interesting reagents of organic and inorganic reaction chemistry are hard-soft "strained" complexes:

Sodium hydride
Lithium aluminium hydride
Lead(IV) acetate
Methyl iodide
Methyl lithium
Triethyloxonium tetrafluoroborate
[Et3O]+ [BF4]


By comparison, the richness of known reaction chemistry arises naturally in the Lewis acid/base interaction matrix, a central tenet of the chemogenesis analysis (but we are in danger of getting ahead of ourselves, see the next pages here & here).

There are two observations/rules, and both concern congeneric arrays of isoelectronic/isoreactive species:

Fajans' Rules

The Pearson-Klopman HSAB analysis is also in direct contradiction with the well known "Fajans' rules" (developed over the years 1915-24), even though no other author appears to have addressed this issue to date.

Ionic-covalent character in metal plus non-metal binary materials can be calculated using the Pauling equation, here, but the difference in electronegativity underestimates the effect of polarisation: the extent to which one atom distorts or polarises the electron cloud of the other.

Fajans rules say:

An example:

Consider beryllium chloride, BeCl2 compared with the other alkaline earth chlorides: MgCl2, CaCl2, SrCl2, & BaCl2:

% Ionic of
to Cl bond
Bond & Material
Ionic Salt
Ionic Salt
Ionic Salt
Ionic Salt

Ionic radius data from web elements

Beryllium chloride, BeCl2, is covalent: the anhydrous material is soluble in organic solvents, it sublimes (in a vacuum), and the molten material is a poor conductor of electricity. MgCl2, CaCl2, SrCl2 and BaCl2 are ionic materials and the molten salts are excellent electrical conductors.

So, What's Going On?

The point is that no physical parameter correlates with hardness over Pearson's chosen set of species. This creates ambiguities, such as with the organic chemistry of the fluoride ion, here, and the contradiction with Fajans' rules, above.

The Pearson model takes no account of FMO geometry (the shapes & phases of the participating orbitals). For example, just how similar are Pearson's hard [Lewis] acids:

H+        [NH4]+      BF3     CO2     Cs+     Cu2+ ?    

Or, how similar are Pearson's soft [Lewis] bases:

 H      R2S:     H3C     benzene ?    

Crucially for organic and main group chemists, the HSAB analysis says little/nothing about the important carbenium ion (carbocation) Lewis acid, H3C+, or the carbanion Lewis base, H3C.

Bold Claim

The one-dimensional hard-borderline-soft continuum of Pearson's analysis actually has the effect of blurring much of the rich, linear (predictable) behaviour that can be found in Lewis acid/base reaction chemistry space.

The new chemogenesis analysis – as presented in this web book and backed by the reaction chemistry held in The Chemical Thesaurus database – avoids and explains the pitfalls of Pearson's much hyped HSAB approach.

Comparing the "Top Down" HSAB Analysis with the "Bottom Up" Chemogenesis Analysis

Pearson's Hard Soft [Lewis] Acid Base (HSAB) analysis is top down.

In contrast, the chemogenesis analysis is bottom up:

The HSAB Papers:

R.G.Pearson, J.Am.Chem.Soc., 85, 3533-3543, 1963
R.G.Pearson, Science, 151, 172-177, 1966
R.G.Pearson, Chem. Br., 3, 103-107, 1967
R.G.Pearson, J.Chem.Ed., 45, 581-587, 1968
R.G.Pearson, Chemical Hardness, Wiley-VCH (1997)

G.Klopman and R.F.Hudson, Theoret. Chim. Acta, 8, 165, 1967
G.Klopman, J.Am.Chem.Soc., 90, 223-234, 1968

Also look here.

Other Post-Pearson Analysis

The ECW model is a semi-quantitative model that describes and predicts the strength of Lewis acid/base interactions. Initially, the model assigned electrostatic (E) and covalent (C) parameters to the Lewis acids and bases. This was later expanded to the ECW model to cover reactions that have a constant energy term, W, which describes processes that precede the acid/base interaction.

In Drago & Wayland's original 1965 analysis, a two term equation was employed such that each Lewis acid is characterized by EA and CA terms and each Lewis base by EB and CB where the E and C parameters refer to the electrostatic and covalent contributions to the strength of the bonds that the acid/base interaction will form. (This is like the Klopman analysis, above.) These parameters were empirically obtained by using enthalpies for adducts that form only σ bonds between the Lewis acid and the Lewis base and have no steric repulsion:


In the ECW model, a new term W was added to the equation.


where the W term represents a constant energy for cleavage of a dimeric Lewis acid or Lewis base.

From An Overview of Lewis Basicity and Affinity Scales by Laurence, Graton & Gal: J. Chem. Educ. 2011, 88, 12, 1651–1657:

The impossibility of establishing a universal scale of Lewis basicity does not prevent the determination of the quantitative behavior of Lewis bases, thanks to scales constructed against particular Lewis acids: BF3, 4-FC6H4OH, I2, Li+, Na+, K+, Al+, Mn+, CpNi+, and CH3NH3+. These scales encompass important types of bonds formed in a Lewis acid–base adduct: the dative bond, the conventional and ionic hydrogen bonds, the halogen bond and cation–molecule bonds for metal cations of groups 1, 7, 10, 11, and 13. Moreover, although these scales are generally not interrelated, there exist family-dependent relationships that permit ranking, in a rather general order, of [Lewis] bases belonging to a given chemical family, for example, the family of oxygen bases. Therefore, the scepticism about the quantitative usefulness of the Lewis concept of acids and bases is no longer founded.

The formation of Lewis acid–base adducts covers a wide variety of bond-forming processes, from the weak van der Waals bond in Ar---BF3 to the strong dative bond in H3N–BF3. The term "bond" can be objectionable for weak adducts. These weakly bonded species are generally produced in a supersonic beam or a cryogenic matrix. Here, we are mainly interested by complexes that can be observed in a room temperature mixture of the Lewis acid and of the Lewis base.

In water, the order of complexation constants of halide ions with the acid Fe3+ is F > Cl > Br > I, whereas with Hg2+, it is I > Br > Cl >F. This reversal is explained by the hard and soft acid and base principle of Pearson.

The coordination of a series of azines to metallocenes has been correlated to the hydrogen-bond basicity scale of the azines.

The ab initio computation of the Lewis acid strength of covalent metal halides in vacuo using the fluoride anion as the reference Lewis base.

A DN value of triethylamine was estimated from a correlation between DN and the NMR chemical shift of the 23Na nucleus for solutions of sodium salts in basic solvents. Later on, the direct determination gave a value that was half the estimated value.

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Lewis & Brønsted Theories of Acidity Main Group Elemental Hydrides

© Mark R. Leach 1999 –

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