The Drago Four-Parameter Equation

One of the main objections to the hard-soft approach to many types of interactions is that it is qualitative in nature. That is, in fact, one of its strengths, and predictions can be made as to how many processes will take place without resorting to calculations. Although this is still largely true, attempts have 

0 Values compiled from C Kittel (1986). Introduction to Solid State Physics, 6th ed,p. 371 Wiley, New York L. Pauling (1970). General Chemistry, 3rd ed., p.  

Freeman, San Francisco and D.RLide (1991). Handbook of Chemistry and Physics, 72nded.,pp 10- 197 to 10-201. CRC Press, Boca Raton, FL  

In the case of the four-parameter equation, the enthalpies of interaction of a large number of acids and bases were determined calorimetrically in an inert solvent. With these values being known, a value of 1.00 was assigned for EA and CA for the Lewis acid iodine. The experimental enthalpies for the interaction of iodine with several molecular Lewis bases were fitted to the data to determine EB and CB values for the bases. Values were thus established for the four parameters for many acids and bases so that they can be used in Eq. (9.112) to calculate the enthalpies of the interactions. The agreement of the experimental and calculated enthalpies is excellent in most cases. However, the four-parameter approach is used primarily in conjunction with interactions between molecular species, although extensions of the approach to include interactions between charged species have been made. Table 9.7 gives the parameters for several acids and bases. 

One of the problems encountered when dealing with the interaction of Lewis acids and bases in a quantitative way is in evaluating the role of the solvent. Bond energies in molecules are values based on the molecule in the gas phase. However, it is not possible to study the interaction of many Lewis acids and bases in the gas phase because the adducts formed are not sufficiently stable to exist at the temperature necessary to convert the reactants to gases. For example, the reaction between pyridine and phenol takes place readily in solution as a result of hydrogen bonding  

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Hydrogen bonding is a special type of acid-base interaction (see Chapter 9). Probably the most important equation relating hydrogen bond strengths is the equation known as the Drago four-parameter equation,... 

Table 9.7 Acid and Base Parameters for Use in the Drago Four-Parameter Equation.

Drago s concept has the merit that two specific factors governing the solvent effect are written together in one common equation. As seen above, characterization of the solvent effect by means of this model succeeded well in certain systems, and less well in others. It appeared that replacement of the two-parameter approach by several parameters might lead to a more generally valid solution. For a joint description of non-specific and specific effects, Koppel and Palm [Ko 72] proposed the introduction of the following four-parameter equation ... 

A four-parameter equation for predicting the calorimetric enthalpies of acid-base interactions, —Ai/ab, in neutral solvents, proposed by Drago et al. [146], with spectroscopically determined shifts of the OH stretching frequency of phenol when interacting with a variety of bases of dilute solutions in carbon tetrachloride and tetrachloroethylene. 

Doan and Drago [153,154] have reported an extended work that Eq. (61) include the spectral shifts obtained from the LSERs approach. They showed that a four-parameter equation for a general set of electron donors (acceptors), in which the specific interaction or spectral shift with an electron acceptor (donors) can be fit by LSERs. 

Drago has proposed a four-parameter equation designed to predict acid-base reaction enthalpies in the gas phase or in poorly solvating media ... 

Drago proposed a four-parameter equation to predict the heat of add base adduct formation [31] ... 

Similar to the perturbation theory, Drago and Wayland proposed a four-parameter equation for predicting reaction enthalpies between acid and base species (Drago and Wayland 1965). Both species are each characterized by two independent parameters an E value which measures their ability to partidpate in electrostatic bonding, and a C value which measures their ability to participate in covalent bonding, leading to ... 

Even if Drago s concept is an attempt to circumvent the quantum mechanical consideration of bond formation, the major importance of the above four parameters is their relationship with the HSAB principle. Actually, through the plot of Ea versus Ca for several liquids on a solid one can obtain indirectly the values of the chemical softness I/77 from the slope of C/E, as represented by the following equation ... 

The double-scale four-parameter enthalpic equation proposed in 1965 (54) and successfully developed by Drago et al seems to be the best tool so far available for correlating and predicting the formation enthalpies of Lewis adducts in the gas phase or, if really necessary, in solution. 

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