7.3.2: HSAB Quantitative Measures (2023)

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    The explanation of trends in metal distribution, solubility of halide salts, and preferred metal coordination patterns is rooted in the observation by Arland, Chatt, and Davies thatLewis acids and bases can be classified into two groups based on their propensity to form stable compounds with each other.(for example.acids of one class tend to form more stable adducts with the bases of the same class than with the bases of the other).1Arland, Chatt, and Davies boringly named these groups Class A and Class B, but today they are known by the Ralph Pearson name to them. Pearson called Class A acids and bases hard and Class B acids and bases soft. These terms reflect how "smooth" the electronic clouds of these substances are in relation to distortion or, in other words, to their polarizability (Figure \(\PageIndex{1}\)). Pearson names acids and bases that are relatively polarizablesoftand those who are hard to polarizestand.

    7.3.2: HSAB Quantitative Measures (1)

    Recognizing hard and soft acids and bases

    Hard acids and basescome in two varieties:

    1. sites of hard acids and bases that have few valence electrons and for which polarization therefore involves distorting the core electrons, which are difficult to distort because they are close to the nucleus and experience a high nuclear charge. The most common examples of such substances are the hard Lewis acids on the left of the periodic table.
    2. hard acid and base sites with a high charge density (highly charged relative to size) and/or that are electron deficient. In these cases, the polarization involves distorted electrons that already experience strong unshielded electrostatic interactions.

    acids and bases molesalso come in two varieties

    1. Soft acids and bases that have many valence electrons and are therefore more easily polarized. Consequently, all other things being equal, soft acids and bases are most likely to be found in the middle or right of the periodic table.
    2. soft acids and bases with low charge density and/or that are relatively rich in electrons.

    Note that the hard-soft classification should not be thought of as if all hard acids and bases are equally hard and all soft acids and bases are equally soft. There is a graduation in hardness and softness and various acids and bases in between that don't fit neatly into either category. With this caveat in mind, the representativehard, soft and borderline acidsare given below. Notice how they illustrate the trends we've just outlined.

    7.3.2: HSAB Quantitative Measures (2)

    As expected, hard acids tend to be found on the left side of the periodic table and involve higher oxidation states and/or electron-donating substituents, while soft acids are more common on the right side of the periodic table and involve lower oxidation states. and/or electron donating substituents.

    Illustrative hard, soft and borderline basesare given below. Again, notice how these substances illustrate general trends.

    7.3.2: HSAB Quantitative Measures (3)

    Qualitative Estimation of Relative Hardness and Softness of Lewis Acids and Bases

    As can be seen from the examples above,Hard acids are relatively electron-poor and hard bases are electron-rich.since they have comparatively

    • small frontier orbitals, reflecting their relatively small atom/ion/fragment sizes
    • high (for acids) or low (for bases) oxidation states on the base atom, reflected in a large formal positive charge (for acids) or negative formal charge (for bases)
    • low polarizability, due to the loss or gain of substantial numbers of electrons, or the location of
      • positive charge on an electropositive element or an atom containing electron-withdrawing substituents
      • negative charge on an electronegative element or an atom containing electron-donating substituents

    Unlike hard acids and bases,soft acids are relatively rich in electrons and soft bases larger and poorer in electronssince they have comparatively

    • large frontier orbitals, reflecting their relatively large atom/ion/fragment sizes
    • low oxidation states, often resulting in small or no atomic charges
    • high polarizability, as would be expected from species in which electron-electron repulsions are smaller and electrons are spread over a large volume. This is sometimes indicated by
      • positive charge on an electronegative element or an atom containing electron-donating substituents
      • negative charge on an electropositive element or an atom containing electron-withdrawing substituents
    Exercise \(\PageIndex{1}\)

    Rank the acids or bases in each set in increasing order of expected hardness.

    1. Cr2+and Cr3+
    2. H+,Cs+, and Tl+
    3. SCN-(acting as a base on N) and SCN-(acting as a base in S)
    4. AlF3, AlH3, AlMe3
    5. The side chains of the following proteinogenic amino acids

    7.3.2: HSAB Quantitative Measures (4)


    (a) Cr2+3+All other things being equal, hardness increases with oxidation state.

    (b) Tl++< H+The order reflects Cs+and Tl+'s larger size compared to H+(which has no electrons that can be polarized in any way) and that Tl+still has two valence electrons while Cs+doesn't have any.

    (c) SCN-(acting as base in S) < SCN-(acting as a base in N). The order reflects N's greater electronegativity than S and N's possession of a more negative formal charge of -1.

    7.3.2: HSAB Quantitative Measures (5)

    (d) AlH3 3 3. Hardness increases as the substituents on the Al center of the Lewis acid become less electron donating and more electron withdrawing (and, incidentally, harder bases) as their electronegativity increases in the H order-< CH3-< F-. Note that the order of electron donating capacity for H-e CH3-the opposite is observed for carbocations, for which hyperconjugation plays a greater role.

    (e) Sec < Cys < Ser. Hardness increases as the electronegativity of the Lewis base chalcogen increases when changing from a selenol to a thiol to an alcohol.

    The Hard-Soft Acid-Base Principle (HSAB Principle)

    OThe hard-soft acid-base principle (HSAB Principle) explains patterns in Lewis acid-base reactivity in terms of ataste reacts with taste preference. Both thermodynamically and kinetically, hard acids prefer hard bases and soft acids prefer soft bases. Specifically,

    • Thermodynamically, hard acids form stronger acid-base complexes with hard bases, while soft acids form stronger complexes with soft bases.
    • Kinetically, hard acids/electrophiles react faster with hard bases/nucleophiles while soft acids/electrophiles react faster with soft bases/neucleophiles.

    Applications of the HSAB principle include

    1. Predicting the balance or speed ofLewisacid-base metathesis and displacement reactions.In a Lewis acid-base metathesis reactionacids and bases exchange partners \[\ce{A1:B1 + A2:B2 <=>[k_1, K_{eq}] A1:B2 + A2:B1} \nonumber \]

    For example, the equilibrium position of the metathesis reaction between \(\ce{TlF}\) and \(\ce{K2S}\) favors the products:

    \[\ce{2TlF + H2S <=>> Tl2S + 2KF} \nonumber \]

    consistent with HSAB's hard-hard and soft-soft preference.

    7.3.2: HSAB Quantitative Measures (6)\[ \no number \]

    The HSAB principle also allows you to predict the position of displacement reactions, in which a Lewis acid or base forms an adduct using a base or acid from an existing Lewis acid-base complex. In these reactions, the displacement of acid or base from the reacting complex can be thought of as a kind of metathesis reaction, in which the unbound acid or base changes places with one in the complex. For example, the reaction between \(\ce{HI}\) and the methylmercury cation

    \[\ce{HI + HgSCH3^{+} <=> CH3SHgI + H^{+}} \nonumber \]

    involves shifting an iodide from \(\ce{HI}\) to give \(\ce{CH3HgI}\). The equilibrium position favors \(\ce{CH3HgI}\) since both \(\ce{CH3Hg^{+}}\) and \(\ce{I^{-}}\) are soft, while \( \ce{H^{+}}\) is a hard acid.

    7.3.2: HSAB Quantitative Measures (7)\[ \no number \]

    Exercise \(\PageIndex{2}\)

    Predict the equilibrium position for the following reaction.

    \[\ce{Fe2O3 + 3Ag2S <=> Fe2S3 + 3Ag2O} \nonumber \]


    Equilibrium will favor the reactants (K<1) as hard-hard and soft-soft interactions in reactants are more stable than hard-soft interactions in products.

    7.3.2: HSAB Quantitative Measures (8)

    Exercise \(\PageIndex{3}\)

    Predict whether \(K\) for the following equilibria will be <<1, ~1 or >>1.

    1. \(\ce{2HF + (CH_3Hg)_2S ⇌ 2CH_3HgF + H_2S}\)
    2. \(\ce{Ag(NH_3)_2^+ + 2PH_3 ⇌ Ag(PH_3)_2^+ + 2NH_3}\)
    3. \(\ce{Ag(PH_3)_2^+ + 2H_3B-SH_2 ⇌ 2H_3B-PH_3 + Ag(SH_2)_2^{+}}\)
    4. \(\ce{H_3B-NH_3 + F_3B-SH_2 ⇌ H_3B-SH_2 + F_3B-NH_3}\)

    The. K < < 1, because reacting adducts are hard-hard and soft-soft, while products involve hard-soft interactions.

    B. K>>1, because the reagent complex, silver(I) diamine, is a complex of a hard base, NH3, with the soft acid, Ag+, while the product is a complex of the same soft acid with the soft base phosphine.

    w. K~1, because all adducts between reactants and products involve soft acids and bases.

    d. K>>1 from BH3it is a softer acid than BF3, then it will form a stronger complex with the softer base H2S while the hardest BF3forms a stronger complex with the harder base NH3.

    2. Predict the relative strengths of a given set ofLewis acids or bases toward a specific substrate. Consider, for example, the relative strengths of a BH3, BMe3, by BF3for group 15 hydrides like NH3, PH3, e AsH3. Of the listed boranes, the hardest acid BF3is the strongest acid for the hard base NH3while BH3is the strongest compared to AsH3.

    Exercise \(\PageIndex{4}\)

    Which acid will form the most stable complex with \(\ce{CO}\): \(\ce{BH3}\), \(\ce{BF3}\), or \(\ce{BMe3}\)?


    \(\ce{BH3}\). Since \(\ce{CO}\) forms complexes primarily through its pair of carbon atoms, it is a soft base and therefore will form the strongest complex with the softest Lewis acid.

    Exercise \(\PageIndex{5}\)

    When lactones react with nucleophiles, they can undergo ring opening reactions to give an alcohol or a carboxylic acid, as shown for propiolactone below:

    7.3.2: HSAB Quantitative Measures (9)

    In the above reaction, sterically unhindered alkoxides give one product and sterically unhindered thioalkoxides the other. Explain why this is the case and predict the reaction products between propiolactone and the sodium salts of ethoxide and thioethoxide.


    The two products of the reaction correspond to nucleophilic attack on the two electrophilic carbon centers of lactones. Specifically, the acid is produced by attack on the softer CEUCH center2directly attached to ester oxygen and alcohol by nucleophilic attack on harder CIIIcenter of the carbonyl ester.

    7.3.2: HSAB Quantitative Measures (10)

    Consequently, it is reasonable to expect that the harder base ethoxide will nucleophilically attack the harder carbonyl carbon, while the softer thioethoxide will attack the softer methylene carbon.

    7.3.2: HSAB Quantitative Measures (11)

    The theoretical interpretation of the hard-soft acid-base principle is that hard-hard preferences reflect superior electrostatic stabilization, while soft-soft preferences reflect superior covalent stabilization.

    The hard-hard and soft-soft preferences in Lewis acid-base interactions reflect that

    • The lone pair of a hard base is strongly electrostatically stabilized by a hard acid.
    • The lone pair of a soft base is strongly stabilized by forming a covalent bond with a soft acid.
    • The lone pair of a hard or soft base is comparatively weakly stabilized by an acid opposite to it in hardness or softness, since the general electrostatic and covalent stabilization of the adduct is comparatively weak.

    To see why this is the case, it is useful to divide the contributions to the interaction energy between an acid and a base as follows:

    7.3.2: HSAB Quantitative Measures (12)\[ \no number \]

    Of the three contributions to the interaction energy, only the ionic and covalent terms directly relate to the hardness of the interacting acid and base. One approach to thinking about how hardness influences ionic and covalent contributions is to consider the boundary orbitals involved in acid-base interaction. This is sometimes done using the Salem-Klopman equation,1,* although in the following treatment a more qualitative approach will be employed.

    Both hard acids and bases will have comparatively low energy HOMO levels and high energy LUMO levels, with a correspondingly high HOMO-LUMO gap. In contrast, soft acids and bases will have comparatively high-energy HOMO levels and low-energy LUMO levels, giving a comparatively smaller HOMO-LUMO gap.

    7.3.2: HSAB Quantitative Measures (13)

    Given this, consider the orbital boundary interactions involved in the formation of an acid-base complex for the possible cases, as illustrated schematically below.

    7.3.2: HSAB Quantitative Measures (14)

    The large energy gap between the highly stabilized HOMO lone pairs of hard bases and the high-energy LUMO of hard acids ensures that, inhard acid-base adducts the dominant stabilizing interaction will involve electrostatic attraction between the lone base pair and the electropositive Lewis acid center. Fortunately, because electron clouds in hard bases are relatively dense and electron-rich, while hard Lewis acids are highly charged and small, these electrostatic interactions are strong.

    In contrast, insoft acid-base adducts, the dominant stabilizing interaction will be covalent.That's it because the small energy gap between a HOMO soft base and a LUMO soft acid allows for the formation of a well-stabilized bonding orbital with significant electron density between the acid and the base.

    The orbital interactions between hard acids and soft bases and soft acids and hard bases are intermediate between the hard acid-hard base and soft acid-soft base cases.

    7.3.2: HSAB Quantitative Measures (15)

    This means that the adducts are stable with respect to both the free acid and the base – but not as well stabilized as they are in the case of a hard acid and a hard base. In the case of hard acids and soft bases, hard acids are less able to electrostatically stabilize the relatively diffuse electron pair of soft bases and there is not as much covalent stabilization as in adducts of soft acids and bases due to the high energy of the hard acid.


    1. Ahrland, S.; Chatt, J.; Davies, N.R., The relative affinities of ligand atoms for acceptor molecules and ions. Quarterly Reviews, Chemical Society 1958, 12(3), 265-276.

    2. Pearson, R. G., Hard and Soft Acids and Bases. Journal of the American Chemical Society 1963, 85 (22), 3533-3539.

    3. Fleming, I., Molecular orbitals and organic chemical reactions. Reference ed.; Wiley: Hoboken, N.J., 2010.


    * Despite the usefulness of this observation, it is generally important to reduce the potential for observer bias by checking observations such as these against compounds reported in the chemical literature and in databases such as Inorganic Crystal Structure and the Cambridge Crystallographic Databases.

    ** They are very soluble in water, to the point that some solutions are perhaps best described as water-in-halide solutions.

    † This can be predicted based on the relative hardness of the BF3, BR3, he BH3in the list of hard and soft acids. However, for those of you who might be confused as to why H is considered a better electron donor for the purpose of smoothing out a Lewis acid center, while alkyl groups are a better electron donor for the purpose of stabilizing carbocations in chemistry organic, the dominant effect is the lower electronegativity of H relative to carbon (in CH3). The effect of electron donation due to hyperconjugation is not as good for thermodynamically stable bases like BX3/BR3.

    †† For more information on the Salem-Klopman equation, see Fleming, I., Molecular orbitals and organicchemical reflections. Reference ed.; Wiley: Hoboken, N.J., 2010; pp. 138-143.

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