Hammett equation complexes

Because the substituent groups have a direct resonance interaction with the charge that develops in the a-complex, quantitative substituent effects exhibit a high resonance component. Hammett equations usually correlate best with the substituent constants (see Section 4.3). ... 

Pyridine bases are well known as ligands in complexes of transition metals, and it might well be anticipated that the equilibrium constants for the formation of such complexes, which are likely to be closely related to the base strength, would follow the Hammett equation. Surprisingly, only very few quantitative studies of such equilibria seem to have been reported, and these only for very short series of compounds. Thus, Murmann and Basolo have reported the formation constants, in aqueous solution at 25°, of the silver(I) complexes... 

The ability of compounds with double bonds to act both as electron donors and as electron acceptors in charge transfer complex formation is well known (81,82). Hammond (83) has studied the correlations of association constants and of the energy of the charge transfer absorption of 2-substituted-l,4-benzoquinones complexed with hexamethylbenzene with the Hammett equation. Charton (84) has studied the correlation with eq. (2) of association constants of 1-substituted propenes with Ag. ... 

On the analogy of the physicochemical relation, one was led to define a biological Hammett equation which related the equilibrium constant of the drug-receptor complex to the electronic a parameters of the substituents (e.g. chlorine, bromine, methyl, ethyl, hydroxyl, carboxyl, acetyl, etc.) of the drug molecule. Since the equilibrium constant of a drug-receptor complex is reflected by the biological activity, this led to the first extrathermodynamic relationship in QS AR ... 

In order to put the discussion on a more quantitative basis we consider one of the more traditional and conceptually simpler methods. Obviously, when speaking about ligands one must take into account that a ligand can bear different substituents. To correlate the variation of the redox potential of a metal complex with the electronic effects played by the substituents of an aromatic ring ligand one uses the Hammett equation in its electrochemical form ... 

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

Clearly, the multifarious factors at work on SCS in pyridines as well as other aromatics can be matched by the more complex manifestations of the Hammett equation and its extensions to provide some sort of correlation, but no systematic overall correlation or related theory has emerged as yet. 

Pyridines are also well known as ligands in transition metal complexes, and if the equilibrium constants for the formation of such complexes can be related to base strength, it is expected that such constants would follow the Hammett equation. The problem has been reviewed,140 and a parameter S, formulated which is a measure of the contribution of the additional stabilization produced by bond formation to the stabilization constants of complexes expressed in terms of a.141 The Hammett equation has also been applied to pyridine 1 1 complexation with Zn(II), Cd(II), and Hg(II) a,/3,y,<5-tetraphenylporphins,142 143 the a values being taken as measures of cation polarizing ability. Variation of the enthalpy of complexation for adducts of bis(2,4-pentanediono)-Cu(II) with pyridines plotted against a, however, exhibited a curved relationship.144... 

The reaction of vanadium salts (VC14, V202(S04)2, V(OCOMe)4, VO(acac)2) and porphyrin gives a complex which, after work-up, is isolated as a very stable oxovanadium(IV) species, VO(Por) (for VO(OEP), V—O = 1.620(2)A, V—= 2.102A, A(N4) = 0.543 A).17 -21 In the presence of a large excess of nitrogenous ligand such as pyridine and piperidine, it forms a six-coordinate complex with a small equilibrium constant (K = 10 I-10 21 M-1).18 The effect of / substituents on the association constant (Kx) is expressed by the Hammett equation (equation 4). 

Then the differences in rate caused by the electronic effect of the substituent are correlated by the Hammett equation log(kz/kH) = poz, where kz is the rate constant obtained for a compound with a particular meta or para substituent, ku is the rate constant for the unsubstituted phenyl group, and crz is the substituent constant for each substituent used. The proportionality constant p relates the substituent constant (electron donating or wididrawing) and the substituent s effect on rate. It gives information about the type and extent of charge development in the activated complex. It is determined by plotting log(kz/kQ) versus ov for a series of substituents. The slope of the linear plot is p and is termed the reaction constant. For example, the reaction shown above is an elimination reaction in which a proton and the nosy late group are eliminated and a C-N n bond is formed in their place. The reaction is second order overall, first order in substrate, and first order in base. The rate constants were measured for several substituted compounds ... 

The Hammett equation is an LFER that can be demonstrated as follows for the case of rate constants. For an unsubstituted reactant, as a reference reactant, the free energy of transition state complex (TSC) is ... 

Charton (J52) has also applied the extended Hammett equation to the oxidation-reduction potentials of 5-substituted phenanthroline complexes of iron in various acidic media (95, 97, 651) and of bis-5- and 4,7-substituted phenanthroline complexes of copper in 50% dioxane (404). Thus, one should expect an overall similarity between the variations in pAa, stability constant, and oxidation-reduction potential data for the various ligands. The variations in a and )3 values found for various substitution positions and the tautomerism in the LH+ ions show that the correlation need not be good. A similar point may also be made about the comparison of data for the transoid bipyridylium ions and their cis complexes. Plots of A versus pA for various systems (95, 404) show a linear dependence to differing extents. As would be expected, the data for analogous complexes of iron (28), ruthenium (214, 217, 531), and osmium (111, 218, 220) show very good correlation. The assumption (152) that the effects of substituents are additive is borne out by these potential data, where the changes in potential on methyl substitution are additive (97). 

A semiempirical approach, similar, for examples, to the Hammett equation, does not require full understanding of complex molecular interactions in solution. A standard reaction or phenomenon is chosen, and the parameters of this reaction or phenomenon during changes in the solvent are examined. These parameters may be represented by the rate of equilibrium constants of the reaction, but also by, for example, shifts of the maxima in various spectra. The relations of this type most frequently used are the Grunwald-Winstein (50), Swain-Scott (57), Gielen-Nasielski (52), Berson (55), and Drougard-Decroocq (54) equations. 

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