Hardness of Lewis acids

Corma, A., Garcia, H., Primo, A., and Domenech, A. 2004. A test reaction to assess the presence of Bronsted acids and the softness-hardness of Lewis acid sites in palladium supported catalysts. New Journal of Chemistry 28, 361-365. 

Pearson, R.G. (1985) Absolute Electronegativity and Absolute Hardness of Lewis Acids and Bases, J. Am. Chem. Soc., 107,6801-6806. 

Pearson RG (1985) Absolute electronegativity and absolute hardness of Lewis acids and bases. J Am Chem Soc 107 6801-6806... 

Pavan, M., Todeschini, R. (Eds.) (2008). Scientific data ranking methods theory and applications. Data handling. In Science and Technology, 1st ed, Elsevier, Oxford, Vol. 27. Pearson, R. G. (1985). Absolute electronegativity and absolute hardness of Lewis acids and bases. J. Am. Chem. Soc. 107,6801-6806. 

The Hard-Soft-Add-Base (HSAB) theory was developed by Pearson in 1963. According to this theory, Lewis acids and Lewis bases are divided into two groups on one hand hard acids and bases, which are usually small, weakly polarizable species with highly localised charges, and on the other hand soft acids and bases which are large, polarizable species with delocalised charges. A selection of Lewis acids, ordered according to their hardness in aqueous solution is presented in Table 1.3. 

The second important influence of the solvent on Lewis acid - Lewis base equilibria concerns the interactions with the Lewis base. Consequently the Lewis addity and, for hard Lewis bases, especially the hydrogen bond donor capacity of tire solvent are important parameters. The electron pair acceptor capacities, quantified by the acceptor number AN, together with the hydrogen bond donor addities. O, of some selected solvents are listed in Table 1.5. Water is among the solvents with the highest AN and, accordingly, interacts strongly witli Lewis bases. This seriously hampers die efficiency of Lewis-acid catalysis in water. 

Analogous to the classification of Lewis acids and bases in hard and soft species, Ahrland et al. have su ested a division of donors and acceptors into classes a and 6. See Ahrland, S. Chatt, J. Davies, N.R. Quart. Rev. 1958, 77, 265... 

In Chapter 6 we survey what has been accomplished and indicate directions for future research. Furthermore, we critically review the influence of water on Lewis acid - Lewis base interactions. This influence has severe implications for catalysis, in particular when hard Lewis acids and bases are involved. We conclude that claims of Lewis-acid catalysis should be accompanied by evidence for a direct interaction between catalyst and substrate. 

Ahrland et al. (1958) classified a number of Lewis acids as of (a) or (b) type based on the relative affinities for various ions of the ligand atoms. The sequence of stability of complexes is different for classes (a) and (b). With acceptor metal ions of class (a), the affinities of the halide ions lie in the sequence F > Cl > Br > I , whereas with class (b), the sequence is F < Cl" < Br < I . Pearson (1963, 1968) classified acids and bases as hard (class (a)), soft (class (b)) and borderline (Table 1.23). Class (a) acids prefer to link with hard bases, whereas class (b) acids prefer soft bases. Yamada and Tanaka (1975) proposed a softness parameter of metal ions, on the basis of the parameters En (electron donor constant) and H (basicity constant) given by Edwards (1954) (Table 1.24). The softness parameter a is given by a/ a - - P), where a and p are constants characteristic of metal ions. 

Fig. 8. Correlation between Pearson s hardness parameter (7P) derived from gas-phase enthalpies of formation of halide compounds of Lewis acids (19), and the hardness parameter in aqueous solution (/A), derived from formation constants of fluoride and hydroxide complexes in aqueous solution (17). The Lewis acids are segregated by charge into separate correlations for monopositive ( ), dipositive (O), and tripositive ( ) cations, with a single tetrapositive ion (Zr4+, ). The /P value for Tl3+ was not reported, but the point is included in parentheses to show the relative ionicity of Tl(III) to ligand bonds. 

The concept of hard and soft acids and bases ( HSAB ) should also be mentioned here. This is not a new theory of acids and bases but represents a useful classification of Lewis acids and bases from the point of view of their reactivity, as introduced by R. G. Pearson. 

The identification given by Equation 2.6 is consistent with the hard and soft acids and bases principle [12,15-21] established originally by Pearson [22] to explain many aspects of Lewis acid-base chemistry. 

This concept was introduced qualitatively in the late 1950s and early 1960s by Pearson, in the framework of his classification of Lewis acids and bases, leading to the introduction of the hard and soft acids and bases (HSAB) principle [19-21]. This principle states that hard acids prefer to bond to hard bases and soft acids to soft bases. In many contributions, the factor of 1/2 is omitted. The inverse of the hardness was introduced as the softness S=l/rj [22]. A third quantity, which can be expressed as a derivative with respect to the number of electrons is the Fukui function, was introduced by Parr and Yang [23,24] ... 

Drago and co-workers Introduced an empirical correlation to calculate the enthalpy of adduct formation of Lewis acids and bases ( 5). In 1971, he and his co-workers expanded the concept to a computer-fitted set of parameters that accurately correlated over 200 enthalpies of adduct formation ( ). These parameters were then used to predict over 1200 enthalpies of interaction. The parameters E and C are loosely Interpreted to relate to the degree of electrostatic and covalent nature of the Interaction between the acids and bases. This model was used to generalize the observations involved in the Pearson hard-soft acid-base model and render it more quantitatively accurate. 

The thermodynamic tendency of a substance to act as a Lewis acid. The strength of a Lewis acid depends on the nature of the base with which the Lewis acid forms a Lewis adduct. Hence, comparative measures of Lewis acidities are given by equilibrium constants for the formation of the adducts by a common reference base. See Lewis Acid Electrophilicity Hard Acids Soft Acids Acceptor Number... 

The values of absolute hardness, shown in the Tables, are highly satisfactory when compared with the known chemical behaviour of the selected systems. The expected chemical behaviour is well reproduced when the valence shell electrons in the absolute hardness calculation are taken into account. As previously mentioned [3], single atom chemistry is not so significant in terms of Lewis acid-base... 

Chandrakumar, K.R.S. and Pal, S., A systematic study on the reactivity of Lewis acid-base complexes through the local hard-soft acid-base principle, J. Phys. Chem. A, 106, 11775-11781, 20002c. 

The hard-soft acid-base principle is not restricted to the usual types of Lewis acid-base interactions. It is a guiding principle for all types of interactions that species of similar electronic character interact best. Accordingly, we will refer to the principle as the hard-soft interaction... 

---