The Taft steric parameter Es

Taft (1956) used the relative rate constants of the acid catalysed hydrolysis of a-substituted methyl ethanoates to define his steric parameter because it had been shown that the rates of these hydrolyses were almost entirely dependent on steric factors. He used methyl ethanoate as his standard and defined Es as  

Taft steric parameters have been found to be useful in a number of investigations (see section 4.4.4). They also suffer from the disadvantage that they are determined by experiment. This has limited the number of values recorded in the literature. 

The molar refractivity is a measure of both the volume of a compound and how easily it is polarized. It is defined as  

---

MacPhee, J. A., A. Panaye, and J.-E. Dubois, A critical examination of the Taft steric parameter-Es. Definition of a revised, broader and homogeneous scale. Extension to highly congested alkyl groups , Tetrahedron, 34, 3553-3562 (1978). 

Equation 12.22 correlates both the Hammett constant ( -, ) and the Taft steric parameter (Es) of the R-group to the experimental activity of the molecule (log I//50). As with the other examples, the requisite activity and parameter values must be entered into a spreadsheet. The only significant difference in this example is that the Jt-values argument for LINEST must include two columns of data (Figure B.7). One includes the Hammett constant data, and the other is for the Taft steric parameter. 

MacPhee, J.A., Panaye, A. and Dubois, J.-E. (1978b). Steric Effects - I. A Critical Examination of the Taft Steric Parameter - Es. Definition of a Revised, Broader and Homogeneous Scale. Extension to Highly Congested Alkyl Groups. Tetrahedron, 34,3553-3562. 

Realistic prediction of the mutagenic activities of this class of mutagens requires a physicochemical evaluation of steric effects of substituents and the most widely utilised measures of such are Taft steric parameters, Es (Table 17).204,210... 

As Table 1.1 shows, fluorine is the second smallest element, with size approximately 20% larger than the smallest element, hydrogen. Table 1.2 summarizes four steric parameters for various elements and groups (i) Taft steric parameters Es [44], (ii) revised Taft steric parameters E [45], (iii) Charton steric parameters o [46], and (iv) A values [47], The steric parameters, Es, E, and u are determined on the basis of relative acid-catalyzed esterification rates, while the A values are derived from the Gibbs free energy difference calculated from the ratios of axial and equatorial conformers of monosubstituted cyclohexanes by NMR. 

BR is the relative biologic activity under investigation, for example the molar EDr>o or the percent response at a given dose. Log P is the logarithm of the octanol-water partition coefficient, a is the approprite Hammett signa constant (electronic in nature), and Es is the Taft steric parameter. With the important demonstration by Hansch that the partition coefficient is often an additive constitutive property, all of the physical parameers may be obtained from the literature. A second important contribution by Hansch is the recognition that the use of statistical techniques is essential to the analysis of quantitative structure-activity relationships. To develop an equation such as that above, one feeds the... 

Clayton and Purcell have illustrated the predictive utility of this method when applied to selected butyrylcholinesterase inhibitors (94). They obtained quantitative correlations using group dipole moments, and /x in addition to hydrophobic parameters. In addition, Hansch and co-workers have used Taft steric parameters (Es) (60) and pKa values to obtain excellent correlations in various systems (84). E8 has recently been shown to be quantitatively related to van der Waal s radii for symmetrical top-like substituents (98) while pKa values have been used as a measure of electron density distributions (99). Fukuto and co-workers combined Tafts Es and a parameters in a physicochemical approach to the mode of action of organophosphorus insecticides (95). 

Hydrophobic parameters are mostly experimentally obtained log P or calculated log P (C log P), where P is the octanol-water partition coefficient. n is the hydrophobic constant of the substituents. The electronic parameters (Hammett constants) a, a and appHes to substituent effects on aromatic systems and Taft s a appHes to ahphatic systems. Steric parameters are Tafts steric parameter Es, McGowan volume MgVol, van der Waals volume Vw, molecular weight MW. Verloop s sterimol parameters Bl, B5 and L... 

To verify such a steric effect a quantitative structure-property relationship study (QSPR) on a series of distinct solute-selector pairs, namely various DNB-amino acid/quinine carbamate CSPpairs with different carbamate residues (Rso) and distinct amino acid residues (Rsa), has been set up [59], To provide a quantitative measure of the effect of the steric bulkiness on the separation factors within this solute-selector series, a-values were correlated by multiple linear and nonlinear regression analysis with the Taft s steric parameter Es that represents a quantitative estimation of the steric bulkiness of a substituent (Note s,sa indicates the independent variable describing the bulkiness of the amino acid residue and i s.so that of the carbamate residue). For example, the steric bulkiness increases in the order methyl < ethyl < n-propyl < n-butyl < i-propyl < cyclohexyl < -butyl < iec.-butyl < t-butyl < 1-adamantyl < phenyl < trityl and simultaneously, the s drops from -1.24 to -6.03. In other words, the smaller the Es, the more bulky is the substituent. The obtained QSPR equation reads as follows ... 

FIGURE 1.11 Systematic optimization of structural binding and stereorecognition increments of amino acid side chain (Rsa) carbamate residue (Rso)- Dependency of separation factors on the steric bulkiness of amino acid and carbamate residues as quantified by their corresponding Taft s steric parameters Es sa Eg so- (1) ionic interaction (2) jr-jr-interaction (3) hydrogen bonding (4) steric interaction. (Reproduced from M. Lammerhofer et al., J. Sep. ScL, 29 1486 (2006). With permission.)... 

Stewart" proposed a parallel between the rate of esterification of 2-substituted benzoic acids and the molecular weights of the substituents. The nitro group deviated strongly from this relationship. It is the first work to attempt to relate the steric effect of a group to some property that might at least in part be a measure of size. Kindler made the first attempt at defining a set of steric parameters. These parameters were later shown to be a function of electrical effects. The first successful parameterization of the steric effect is due to Taft, who defined the steric parameter Es for aliphatic systems by equation 27 ... 

Here, k and k0 are the rate constants for the reaction initiated by a tertiary amine and a standard tertiary amine, respectively, q is the reaction constant, a are the substituent parameters, 8 is the steric parameter of the reaction and En(En) are steric parameters of the substituents (identical with the Taft s constants ES(E9)). 

Taft steric parameter A Taft steric parameter describes the physical size of a substituent on a parent molecule. Taft parameters, denoted as Es, are often used in Hansch analyses to link lipophilicity changes to biological activity, tag A tag is a signal molecule that is attached to a bead to facilitate deconvolution in molecular libraries prepared by split... 

These quaternization rate constants of 2-alkylpyridines (Me—r-butyl) were correlated by Taft (53JA4538) with the steric parameters Es. 

To characterize the substituents (the X block) a set common substituent parameters were compiled from the literature. These parameters were as (Taft inductive parameter), trp (Hammett parameter for para substituents), F and R (Swain-Lupton dual substituent parameters), Es and Esc (Taft steric parameters), van der Waals radius, L, Bv B2, B3, (Verloop sterimol parameters), MR (molar refractivity), and n (Hansch lipophilicity parameter). Data are given in Refs. [1,19] and are not reproduced here. 

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. 

Steric effects have been recognized as important in organic chemistry since 1872 (6). However, it was not until the 1950s that a meaningful quantification of this steric effect appeared (7). Taft defined a steric parameter, Es, as the average relative rate of acid-catalyzed ester hydrolysis ... 

The alternatives to mathematical descriptors derived from molecular graphs or molecular geometry are the traditional QSAR (quantitative structure-activity relationship) descriptors and quantum chemically computed parameters. The former include the partition coefficient for oil/water (often octanol/water) (log P), the Hammet sigma value (electronic parameter that measures the electron withdrawal from and the electron release to the aromatic ring by a substituent, the Taft s parameters for the electronic effects of substituents in aliphatic compounds (a ), and a steric parameter for the proximity of substituents on reaction sites (Es)- Also selected molecular properties, such as molar refractivity (MR), polarizability (a), molecular weight (MW), and density (d), have been used. 

We have remarked above that the Taft Es values suffered from a number of deficiencies. In fact, the only direct evidence that they were a measure of steric effects was their successful correlation with rv values, a correlation limited to symmetrical top tetrahedral substituents such as CH3 and CF3 and to H. The evidence presented above indicates that rv values are a useful measure of steric effects and suggested that they might be used directly as steric parameters in correlation analysis. They were so used by Charton 6,n,13,14). They did meet the first and third criteria for steric parameters in full and the fourth in part. They did not meet the second, fifth and sixth, however. The Taft Es values met the first criteria only if it could be assumed that the use by Taft of average values of data obtained under different experimental conditions was valid. Our results indicate that this is not the case. Es values did meet the third condition, but were unable to meet the other criteria. It seemed more reasonable to base a set of steric parameters on the van der Waals radii than to do so upon Es values and to attempt to remove their deficiencies. By defining a set of steric parameters, designated values, from the equation... 

In his calculation of Es values, Taft made use of average values of log (krx/kr0). Evidence has been presented which suggests that this procedure is unjustified, as the dependence of log kvx/kvo0) on X is not independent of medium. Effective values, oef, of the steric parameter for some ICD groups have been obtained by means of a two step procedure, 24, 25 ... 

In the following years, various steric parameters have been applied to the analysis besides the Taft Es value. For instance, the Hancock corrected steric E , the Bondi molecular volume Vw, and the Verloop STERIMOL parameters have been used to rationalize various steric effects depending upon the interactions involved. At every addition of such parameters, the versatility of the approach has been expanded remarkably. The number of successful applications has been growing enormously leading to the present state of development. 

These Es parameters estimated by Eq. 4 for hetero atom substituents can be combined with those originally developed for various alkyl groups as a set of steric constants for QSAR studies of aromatic systems 6). Thus, apart from the original definition for the intramolecular steric effect, the combined set of Es parameters is able to represent intermolecular steric effects as well. The original Taft E, values for unsymmetrical alkyl groups seem to represent effective steric dimension of the groups which is scaled on the same standard as those for symmetric monoatomic substituents where the effective dimension coincides with the van der Waals radius. 

A quantitative correlation of structural effects of four esters and four alcohols in the vapour phase transesterification on a macroreticular ion exchanger at 120°C was made using the Taft equation [441]. The authors found that rate coefficients [from eqn. (27)] yielded better correlation with steric (Es) than with polar (a ) parameters, while there was no significant difference between the correlations of the adsorption coefficients of alcohols, Kb, with both parameters. The correlations with Es yielded the slopes 1.4 and 0.6 for the reactivity of the esters and the alcohols, respectively, and —0.4 for the adsorptivity of the alcohols. The observed... 

The hydroxide anion catalyzed rate constants for the scries of alkyl tris-(2-methoxyethoxy)silanes obtained by Fohl were used to define a modified Taft equation, log(/cHO//cHO ) = 2.48cr +1.67 Es [42], A good correlation was obtained, except for vinyl and phenyl substituents. The anomalous behavior observed for phenyl and vinyl tris-(2-methoxyethoxy)silanes may have resulted because the steric parameter or the polar parameter may be influenced by the carbon-carbon double bond. The steric parameter for a,yS-unsaturated substituents may include an appreciable resonance effect. The polar parameter values may be influenced by the ability of silicon to back-bond through d orbitals with the a,/J-unsaturated system [37,49]. 

Taft s o has nearly the same meaning as Hammett s c (with different numerical values), Es is the steric parameter for substituent X, and 8 is a measure of the sensitivity of the reaction to changes in steric properties near the reaction center (similar to p). Extensive compilations of values of o, o and Es appear in Perrin et al. (1981) and McPhee et al. (1978), respectively. 

Examples for compounds are given in Figure 8.1, and the regression analysis equation is provided below for the QSAR of triazine derivatives in photosynthesis (Draber, 1992). The inhibitory potency expressed as a pl50 value is equal to a lipophilicity parameter tt (log of the partition coefficient P), an electronic substitution parameter a (the Hammett constant) and to a lesser degree to a steric component Es (the Taft constant). 

The chiral discrimination found in the minima and TS structures of these dimers are gathered in Table 3.3. Herein, no clear tendency was observed with a relatively large number of homochiral dimers (R,R or SS) being more stable than its corresponding heterochiral ones. Attempts to explain these results based on secondary interactions using the AIM methodology resulted in poor correlations with steric parameters such as Taft s Es, an indication that a more complex mechanism controls these energetic differences. 

---