HSAB Quantitative Measures

There are two major HSAB quantitative measures. One, developed by Pearson, uses the hard-soft terminology and defines the absolute hardness, 17, as half the difference between the ionization energy and the electron affinity (both in eV)  

Idealized Hard Species Add A B Base Hard—Hard Interaction Idealized Soft Species Acid A B Base Soft-Soft Interaction 

This definition of hardness is related to Mulliken s definition of electronegativity, called absolute electronegativity by Pearson  

This approach describes a hard acid or base as a species that has a large difference between its ionization energy and its electron affinity. Ionization energy is assumed to measure the energy of the HOMO, and electron affinity is assumed to measure the LUMO for a given molecule  

Softness is defined as the inverse of hardness, a = —. Because there are no electron 

---

They indicated that the softness parameter may reasonably be considered as a quantitative measure of the softness of metal ions and is consistent with the HSAB principle by Pearson (1963, 1968). Wood et al. (1987) have shown experimentally that the relative solubilities of the metals in H20-NaCl-C02 solutions from 200°C to 350°C are consistent with the HSAB principle in chloride-poor solutions, the soft ions Au" " and Ag+ prefer to combine with the soft bisulfide ligand the borderline ions Fe +, Zn +, Pb +, Sb + and Bi- + prefer water, hydroxyl, carbonate or bicarbonate ligands, and the extremely hard Mo + bonds only to the hard anions OH and. Tables 1.23 and 1.24 show the classification of metals and ligands according to the HSAB principle of Ahrland et al. (1958), Pearson (1963, 1968) (Table 1.23) and softness parameter of Yamada and Tanaka (1975) (Table 1.24). Compari.son of Table 1.22 with Tables 1.23 and 1.24 makes it evident that the metals associated with the gold-silver deposits have a relatively soft character, whereas those associated with the base-metal deposits have a relatively hard (or borderline) character. For example, metals that tend to form hard acids (Mn +, Ga +, In- +, Fe +, Sn " ", MoO +, WO " ", CO2) and borderline acids (Fe +, Zn +, Pb +, Sb +) are enriched in the base-metal deposits, whereas metals that tend to form soft acids... 

The major disadvantage of the HSAB principle is its qualitative nature. Several models of acid-base reactions have been developed on a quantitative basis and have application to solvent extraction. Once such model uses donor numbers [8], which were proposed to correlate the effect of an adduct on an acidic solute with the basicity of the adduct (i.e., its ability to donate an electron pair to the acidic solute). The reference scale of donor numbers of the adduct bases is based on the enthalpy of reaction. A//, of the donor (designated as B) with SbCb when they are dissolved in 1,2-dichloroethane solvent. The donor numbers, designated DN, are a measure of the strength of the B—SbCb bond. It is further assumed that the order of DN values for the SbCb interaction remains constant for the interaction of the donor bases with all other solute acids. Thus, for any donor base B and any acceptor acid A, the enthalpy of reaction to form B A is ... 

In our original work, we used an ionic-covalent model to interpret the E and C parameters. It has been suggested that our E and C parameters are a quantitative manifestation of the hard-soft model. "Softness (or hardness") can be considered (67) as a measure of the ratio of the tendency of a spedes to undergo covalent interaction to the tendency of the species to undergo electrostatic interaction. The relative "softness or hardness is depicted in the C/E ratio. The ratios for the acids and bases can be calculated from the data in Tables 3 and 4. If the ratio C/E is comparatively large, the add or base would be classified as type B or soft. Inasmuch as the relative ratios of C/E tells the relative importance of the two effects for various donors and acceptors, we agree that the hardness or softness discussed in the HSAB model is given by this ratio. 

Unfortunately this equation is as quantitative as HSAB gets. There was no exact definition of hardness, ry, and no operational definition which allowed it to be measured. The values in Tables 1.4 and 1.5 are useful only in ordering acids and bases. They are not transferable as numbers to any other examples. Therefore applications have always been qualitative. Even so, the HSAB concept has been extremely useful in correlating and understanding a great deal of experimental data. 

In the beginning when the HSAB principle was Just introduced, the meaning of hardness was not easy to understand. Certainly, it is not the hardness that measures the resistance against deformation. Then, what is it It was not un il the last several years that the real definition of absolute hardness received a quantitative and theoretical backing. ... 

---