Extended Hansch Equations

Px and Ph represent the partition coefficients of a derivative and the parent molecule, respectively. Fujita and Hansch then combined these hydrophobic constants with Hammett s electronic constants to yield the linear Hansch equation and its many extended forms (19). 

Hundreds of equations later, the failure of linear equations in cases with extended hydrophobicity ranges led to the development of the Hansch parabolic equation (20) ... 

More than a hundred years ago, Meyer and Overton made their seminal discovery on the correlation between oil/water partition coefficients and the narcotie potencies of small organic molecules (7,8). Ferguson extended this analysis by placing the relationship between depressant action and hydrophobicity in a thermodynamic context the relative saturation of the depressant in the biophase was a critical determinant of its narcotic potency (9). At this time, the success of the Hammett equation began to permeate structure-activity studies and hydrophobicity as a determinant was relegated to the background. In a landmark study, Hansch and his colleagues de-... 

The Taft-Kutter-Hansch steric constants (TKH Es) constitute a combined set of parameters of the original Taft steric constants and those extended by Kutter and Hansch [Kutter and Hansch, 1969 Hansch, 1970 Sotomatsu and Fujita, 1989] by using a correlation with the average of the minimum and maximum van der Waals radii as defined by the equation ... 

Often it is convenient to derive first a Hansch model for a small, chemically closely related subset and then to extend this equation to larger sets of compounds. For the papain binding of benzamido-glycine and mesylamido-glycine phenyl esters, with different substituents at the phenyl ester group, Eq. (44) was derived for the benzamides and Eq. (45) for the mesylamides [77] ... 

Another type of parameter that often appears in published QSAR equations is an indicator variable. Indicator variables are used to extend a QSAR equation over a variety of different types of molecule and so make the equation more generally applicable. For example, Hansch and colleagues derived the following equation for the bindmg constants of sulphonamides (X-C6H4-SO2NH2) to human carbonic anhydrase [Hansch et al. 1985] ... 

Another use of rho is to convert sigma values, derived from benzoic acid, for use in other nuclei. This was first achieved for naphthalene the results were then extended to quinoline, and then to other heterocycles [Perrin, 1965c Perrin, Dempsey and Serjeant, 1981 (their Section 7.2)]. Although rho continues to appear in formal statements of Hansch s multiple regression equation, it is usually only indirectly present, namely as a nucleus-modified sigma value. 

Values of a l were calculated from thepKa of 4-substituted-[2.2.2]bicy-clooctane-1-carboxylic acids in 50% w/w ethanol-water at 25 by setting in Equation 41 equal to every odd value in the range 1.45 to 1.67. This range was chosen to include all of the choices of L, which had been made previously from the value of 1.464 used by Roberts and Moreland to the value of 1.65 used by Hansch et al. The corresponding o d values were obtained by means of Equation 42, using the Op values of McDaniel and Brown (28). The a and a o values are given in Table 1. The pKa values reported by Thuaire (30) for 4-substituted benzoic acids in ethanol-water mixtures and in ethanol (Table 2) were correlated with the 12 sets of and a n values obtained above by means of the extended Hammett equation. Also studied were pKa values for 4-substituted benzoic adds in ethanol-water mixtures determined by Wepster (31). The substituents studied are set 7 H, Me, Et, OH, OMe, Cl, Br, NO2, CF3, C02Me Set 8 = Set 7, less CF3 Set 6 = Set 8 less Br. 

Almost every kind of organic reaction has been treated via the Hammett equation, or its extended form." Hansch, C Leo, A. Taft, R, W. Chem. Rev. 1991,91,165. 

This work was extended by Hansch et at. (1971) using a krypton ion laser, and the apparatus shown in Fig.13.13. In this experiment the iodine absorption cell was placed outside the laser cavity and a standing wave was obtained by arranging two laser beams, each of 10 mW power, to intersect at an angle of less than 2 mrad inside the 20 cm long absorption cell. From equation (13.40) the saturated absorption coefficient when both beams are present in the cell is given approximately by... 

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