Hammett equation additional parameters

The additional parameter r is adjusted from reaction to reaction it reflects the extent of the additional resonance contribution. A large r corresponds to a reaction with a large resonance component, whereas when r goes to zero, the equation is identical to the original Hammett equation. When there is direct conjugation with an electron-rich reaction center, an equation analogous to Eq. (4.17) can be employed, but a is used instead of [Pg.210]

Hammett equation(s) 78, 93, 148ff., 151 f., 153ff., 167f., 190, 193, 196, 297, 299, 308, 312, 375, 381, 392, see also Dual substituent parameter, and Quantitative structure-reactivity relationships Hammond postulate, in additions of nucleophiles to diazonium ions 157 Hard and soft acids/bases principle (Pearson) 49, 54, 109... 

Haloform reaction, 237, 296 Halogenation alkanes, 300, 323 alkenes, 179,186, 313 benzene, 138,316 ketones, 295 Hammett equation, 362 additional parameters, 374, 388, 395 derivation of, 362 deviations from, 375 empirical nature of, 395 implications of, 394 reaction pathway, and, 375 solvent effects and, 388 spectroscopic correlations, 392 standard reaction for, 362, 395 steric effects and, 361, 383 thermodynamic implications of, 394 Hammett plots, 359 change in rate-limiting step and, 383 change in reaction pathway and, 378... 

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... 

Several large databases of rate constants (Hendry et al., 1974 Howard, 1972) and several correlation equations, facilitate estimating rate constants for ROz in air or nonpolar solvents, but these data and SARs apply chiefly to hydrocarbons in which H-atom transfers and additions to double bonds are too slow to be important under environmental conditions. SARs for reactions of ROz radicals with phenols mostly in organic solvents, are listed in Table 15,7, along with the SAR parameters for the Hammett equation (Equation 24). Most of these correlations fit best using o+ rather than o, with p values ranging from -1.50 to -0.80. 

From the results summarized in Table I, apparently the Brpnsted relationship will hold for all combinations of nucleophiles and electrophiles. Because, as pointed out previously, the Hammett equation is really a special case of the Brpnsted relationship, all the legion of nucleophile-electrophile, rate-equilibrium Hammett correlations that have been studied also fall under the scope of the Brpnsted relationship. For example, nucleophilicities of ArO , ArS , ArC(CN)2 , and the other families listed in footnote c of Table I have generally been correlated by the Hammett equation, where the acidities of benzoic acids in water are used as a model for substituent interactions with the reaction site (a), and the variable parameter p is used to define the sensitivity of the rate constants to these substituent effects. The Brpnsted equation (equation 3) offers a much more precise relationship of the same kind, because this equation does not depend on an arbitrary model and allows rate and equilibrium constants to be measured in the same solvent. Furthermore, the Brpnsted relationship is also applicable to families of aliphatic bases such as carboxylate ions (GCH2C02 ), alkoxide ions (GCH20 ), and amines (GCH2NH2). In addition, other correlations of a kinetic parameter (log fc, AGf, Ea, etc.) can be included with various thermodynamic parameters (pKfl, AG°, Eox, etc.) under the Brpnsted label. 

Thirty-five compounds provided exact numerical Iso values which could be used in the computations. There are 15 various substituents appearing in five possible substituent positions (numbered I-V in Structure A) in these compounds. In a program, written in BASIC, a descriptor matrix was created by copying the appropriate substituent parameters into the corresponding substitution position-compartments of the descriptor matrix if the actual substituent is present in the molecule in the actual position. From the Hammett constants, the equation - a was assumed (31,, 1 ), thus a was applied for positions I, III and V, and for positions II and IV. Therefore, 10 parameters were used to enter the descriptor matrix for each substituent position. Two additional parameters, the total lipophilicity [J]x] and its square value [(X > ) 1 were also calculated for each compound and were added to the data-set. 

The successful decomposition of a values into field and resonance components could eliminate the need for several sets of o values. The Swain-Lupton system must treat meta- and para-substituted compounds as separate reaction series, with differing values for r and / for a meta versus para placement of the substituent. The reason is that resonance interactions are usually stronger in the para series. There must also be an additional parameter for each reaction, since the relative sensitivity to resonance and field effects differs from reaction to reaction. Swain and Lupton have observed satisfactory correlation for over forty reaction series using and This treatment also provides an indication of the relative importance of resonance and field interactions. The mathematical manipulations are, of course, more complex than in the simple Hammett equation. The Swain-Lupton correlations are carried out by a computer program that provides a best-fit correlation in terms of /, r, and The computation also yields percent resonance by comparing the magnitude of/ andr. 

The various multiparameter equations can usually improve the correlation of data that give poor correlations with the single-parameter Hammett equation. It must be recognized that this in part may be a direct consequence of the introduction of additional variable parameters. To derive solid mechanistic insight into the basis of improved correlation requires a critical appraisal of the results, and statistical analysis may be necessary. The details of critical statistical evaluation of free-energy... 

The absolute rate constants for ene-addition of acetone to the substituted 1,1-diphenyl-silenes 19a-e at 23 °C (affording the silyl enol ethers 53 equation 46) correlate with Hammett substituent parameters, leading to p-values of +1.5 and +1.1 in hexane and acetonitrile solution, respectively41. Table 8 lists the absolute rate constants reported for the reactions in isooctane solution, along with k /k -, values calculated as the ratio of the rate constants for reaction of acetone and acctonc-rff,. In acetonitrile the kinetic isotope effects range in magnitude from k /k y = 3.1 (i.e. 1.21 per deuterium) for the least reactive member of the series (19b) to A hA D = 1.3 (i.e. 1.04 per deuterium) for the most reactive (19e)41. Arrhenius plots for the reactions of 19a and 19e with acetone in the two solvents are shown in Figure 9, and were analysed in terms of the mechanism of equation 46. 

Because spiropyrans (and especially BIPS) are relatively easy to prepare, a variety of compounds are available from which to deduce correlations (usually semiempirical Hammett-like equations) between structure and photochromic parameters in dilute fluid solutions. The photochromic behavior of a single dye in a variety of solvents can also be correlated with a solvent parameter such as. In applications, however, the dyes are almost always relatively concentrated in a bulk polymer or a polymeric binder film, and various other additives such as antioxidants, surfactants, fire retardants, plasticizers, and other colorants are also present. Under these conditions, the observed photochromic behavior is often very different from that predicted by the dilute fluid solution correlations. 

Px is the partition coefficient of a derivative and PH is that for the parent compound.) Also used were Hammett s o- constant, Taft s polar constant, steric parameter, Es. In a few examples (Equations 17, 21, 24, and 30), P values from oleyl alcohol/water have been used. In one instance (Equation 69) the chemical shift of a phenolic proton has been used for comparison with the a constant. Where possible, the experimentally measured partition coefficients for all members of the series have been used. In other instances only one member of a set has been measured. Values for the other members were obtained by taking advantage of the additivity principles of log P and tr. Details are given elsewhere (4, 7, and 8). For the new work of Table II, log P values for the parent compounds are given in the footnotes. 

Several two-parameter equations have been suggested based on the additivity of I and R effects, each being the combination of various components as described earlier. Taft originally introduced this approach for the electronic effects of benzene and defined Or values employing values of Oj (from the aliphatic series - see Chapter 2) and Hammett s a for para substituents (Equation 18). 

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