The Extrathermodynamic Approach Hansch Analysis

For in vivo data eq. 61 was extended to eq. 62 by including a parabolic lipophilicity term. The idea behind eq. 62 was that molecules which are too hydrophilic or too lipophilic will not be able to cross lipophilic or hydrophilic barriers, respectively. Therefore, they will have a lower probability to arrive at the receptor site than molecules with intermediate lipophilicity, being readily soluble in aqueous phases as well as in lipid phases. 

61 and 62 are only two examples of an enormous wide variety of Hansch equations. Later steric parameters were added to this general model and even later molar refractivity values. With such multiparameter equations it was possible to 

Only one illustrative example is given here to describe and explain the proper application of Hansch analysis (for further examples see chapter 7). Graham and Karrar [397] determined the antiadrenergic activities of a series of a-bromo-phenethylamines (8). Hansch and Lien [398] derived eq. 63, which was at this time considered to give the best quantitative description of the data (Table 12 only some 

Later Cammarata [399] presented eq. 64 (recalculated) which describes meta-substituents by their n and a values and para-substituents by a steric parameter However, the steric parameter has the wrong sign the positive value of its regression coefficient implicates that steric bulk increases biological activity, which cannot be true. In addition, it is difficult to understand how an electronic effect can only be obtained for the wc/a-substituents. 

Correspondingly, eq. 64 was criticized by Unger and Hansch [307] in a noteworthy paper, which constitutes a milestone in the development of Hansch analysis. They formulated rules for the derivation of extrathermodynamic equations which are summarized here because of their general validity (supplementary comments are given in parentheses)  

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