Enthalpies of adduct formation

Drago and co-workers have correlated a large body of enthalpies of adduct formation in Lewis acid-base systems, including some solvents as reactants, with this four-parameter equation ... 

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. 

Next, a quantitative model, referred to as the E and C equation, is presented for predicting and correlating the enthalpies of adduct formation. The use of this equation and the interpretation of the parameters which result is discussed. Exceptions to the correlation are considered and the valuable insight about intermolecular interactions that can be gained by firmly establishing these exceptions is demonstrated. The parameters we obtain and valid transformations of these parameters are considered in the light of both the HSAB model and Donor Strength model of acid-base chemistry. Both of these concepts are shown to be at best incomplete models of coordination. The relationship between our parameters and the a—q Hammett parameters is quantitatively demonstrated. 

I) The selection of the enthalpy of adduct formation, as an approximation to the change in internal energy of the donor and acceptor upon addition compound formation, results from the thorough discussion by J. E. Leffler and E. Grunwald in Rates and Equilibria of Organic Reactions, New York John Wiley 1963. 

It has been reported 2d) that the spectrophotometric determination of the enthalpies of adduct formation for sulfur donors with iodine produce the same result (within experimental error) in cyclohexane or CCI4, but these donors with various acids invariably give low results in CCI4 by a constant amount when measured calorimetrically 10). Treating the problem as one involving competing equilibria, we can describe the interaction between the base and CCI4 as ... 

In the spectrophotometric determination of enthalpies of adduct formation, one usually measures the equilibrium concentration of [AB] or [A]. Following a treatment of competing equilibria reported by Tamres 25) consider the effect of base-solvent interaction on this experiment when one investigates the properties corresponding to the free and complexed acid. Now, [AB] can be determined even if the base interacts with the solvent, say CCI4. Again, describing the system by equation ... 

These qualitative explanations, whether they be hard-soft or ionic-covalent or Class A-Class B, all suffer from the arbitrary way in which they can be employed. All Lewis acid-base type interactions are composed of some electrostatic and some covalent properties, i.e., hardness and softness are not mutually exclusive properties. Predictions are straightforward when dealing with the extremes, but with other more ambiguous systems, one can be very arbitrary in explaining results and the predictive value is impaired. What is needed is a quantitative assessment of the essential factors which can contribute to donor strength and acceptor strength. Proper combination of these parameters should produce the enthalpy of adduct formation. Until this can be accomplished, one could even question the often made assumption that the strength of the donor-acceptor interaction is a function of the individual properties of a donor or acceptor. 

In 1965, the following double-scale equation was proposed (39) to correlate enthalpies of adduct formation in the gas phase and poor solvating solvents ... 

The parameters calculated for the acids are given in Table 3 and those for the bases in Table 4. The weighted root-mean-square deviation between the experimental enthalpies and those calculated from the parameters in Tables 3 and 4 using Eq. (13) is about 0.016 corresponding to a deviation of about 0.2 kcal/mole for a heat of 8 kcal/mole. The excellent agreement between the experimental enthalpies of adduct formation and the calculated enthalpies for aU of the interactions are reported in the literature (40). 

As mentioned above, the initial model (39) was chosen so as to break the enthalpy of adduct formation into electrostatic and covalent contributions, i.e., — AH =EaEb- -CaCb. The fact that more than one solution can exist enables us to attempt to break-up the enthalpy of adduct formation into a physically meaningful model other than the electrostatic and covalent model initially employed. One apparently obvious break-up of the enthalpy of adduct formation which is of chemical interest would be that of sigma, tr, and pi, n, contributions ... 

In addition, rearranging Eq. (21) and combining with Eq. (19) illustrates that i = k" y. Therefore, a two parameter (one term) model would require that a plot of the enthalpies of adduct formation of one acid versus the enthalpies of adduct formation of another acid for the same series of bases be linear with a zero intercept. The enthalpies of adduct formation for 12 and phenol with a wide series of bases does not give rise to such a plot as can be seen in Fig. 5. These acids have very different C/E ratios and their enthalpies of adduct formation cannot be correlated by a one term model. Furthermore, a one term model could riot incorporate systems in which reversals in donor-acceptor strength are observed 32). However, it is possible to correlate enthalpies of adduct formation for acids with very similar C/E ratios such as hydrogenbonding acids using a one term equation. Correlations restricted to one particular type of acid are, of-course, only a subset of the overall E and C correlation. 

To put Eq. (23) in the form of that of the Hammett equation for a series of substituted phenols, the restriction — AHb =CaCb is required where AHb is the enthalpy of adduct formation for a given base with unsubstituted phenol. Now Ea is comparable to a and Ejb is comparable to q. Using the transformation Eq, (16) and (17), this restriction in terms of the unprimed E and C parameters is given by... 

One very important use of E and G numbers is the calculation of heats of interaction for systems which have not been examined experimentally. We are now in a position to predict almost 1000 enthalpies of adduct formation by combining the parameters in Tables 3 and 4 according to Eq. (13). The trimethylaluminium enthalpies are for the monomer... 

A very interesting system which serves as a splendid example of many of the points made so far concerns the acid methylcobaloxime. Methylcobaloxime is a dimer in non-basic solvents. The solvation minimized enthalpies of adduct formation corrected for the enthalpy of dimerization of methylcobaloxime (55) are presented in Table 6. 

Table 6. Enthalpies of adduct formation toward methylcobaloxime monomer...

Although these correlations could be extended to the acid pyrrole, we were not able to get a linear plot of Avc-n vs. the enthalpy of adduct formation with the acid chloroform (23). Furthermore, we did not obtain a straight line Avc-n vs. Avq-h(phenol) plot. 

Many of the studies with amides have included evaluation of ligand-field parameters if appropriate. The differences between different amides are quite small. For [NiL6]2+, Dq varies from 749 cm-1 when L is A-methylcaprolactam to 850 cm1 when L is DMF.44,45 However, the spectro-chemical order in complexes [U02L5]2+ is DMA < NMA as DMF < NMF65 compared with NMA < DMA 4 NMF < DMF for Ni2+ neither series follows the order of donor strengths reflected by the Gutmann donor numbers, which rank DMA marginally above DMF as a donor in terms of the enthalpies of adduct formation with SbCls-66... 

Parameter Equation for Predicting Enthalpies of Adduct Formation. 

The original set of E and C parameters was determined mainly with the help of enthalpies of adduct formation of iodine and phenol as acceptors with alkylamines as donors. Subsequently, the best set of E and C parameters has been obtained by computer optimization of a large data base of enthalpies and four arbitrarily fixed reference values [71, 215] E = C = for iodine, E = 1.32 for A, A -dimethylacetamide, and Cb = 7.40 for diethyl sulfane. Table 2-6 gives a selection of E and C parameters for Lewis acids and bases commonly used as solvents. 

Calculate the enthalpy of adduct formation predicted by Drago s E, C equation for the reactions of I2 with diethyl ether and diethyl sulfide. 

Boron-containing Heterocycles.—The enthalpies of adduct formation between pyridine, 2-picoline, 4-picoline, or 2,4,6-collidine and a number of heterocyclic boron derivatives (2-Br- or 2-organo-l,3,2-dihetero-borolans, -borinans, and -boroles) have been measured.282 The presence of Br greatly increases the Lewis acidity of the B atom. 

A double-scale enthalpy equation proposed by Drago and Wayland to correlate (and predict) the enthalpy of adduct formation in gas-phase or poorly solvating media [17,18] is given by ... 

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